Q1. What is reflection of light?

Answer: Reflection is the bouncing back of light into the same medium after striking a smooth or polished surface.

Q2. State the first law of reflection.

Answer: The angle of incidence is equal to the angle of reflection.

∠i = ∠r

Q3. State the second law of reflection.

Answer: The incident ray, reflected ray and normal at the point of incidence all lie in the same plane.

Q4. What is a spherical mirror?

Answer: A mirror whose reflecting surface is a part of a hollow sphere is called a spherical mirror.

Q5. What is a concave mirror?

Answer: A spherical mirror whose reflecting surface is curved inward is called a concave mirror.

Q6. What is a convex mirror?

Answer: A spherical mirror whose reflecting surface is curved outward is called a convex mirror.

Q7. What is pole of a spherical mirror?

Answer: The centre of the reflecting surface of a spherical mirror is called its pole. It is denoted by P.

Q8. What is principal axis?

Answer: The straight line passing through the pole and centre of curvature of a spherical mirror is called the principal axis.

Q9. What is aperture?

Answer: The diameter of the reflecting surface of a spherical mirror or refracting surface of a lens is called aperture.

Q10. Write the relation between radius of curvature and focal length of a spherical mirror.

Answer:

R = 2f

Q11. What is refraction of light?

Answer: Refraction is the bending of light when it passes obliquely from one transparent medium to another.

Q12. State Snell’s law.

Answer: For a given pair of media, the ratio of sine of angle of incidence to sine of angle of refraction is constant.

sin i / sin r = constant

Q13. What is absolute refractive index?

Answer: Absolute refractive index of a medium is the ratio of speed of light in vacuum to the speed of light in that medium.

n = c / v

Q14. What is power of a lens?

Answer: Power of a lens is the ability of the lens to converge or diverge light rays. It is reciprocal of focal length in metres.

P = 1 / f

Q15. What is the SI unit of power of lens?

Answer: Dioptre, denoted by D.

Q1. A ray of light strikes a plane mirror at an angle of incidence of 35°. What will be the angle of reflection?

Answer: According to the law of reflection, angle of incidence is equal to angle of reflection.

∠i = ∠r = 35°

Q2. Why are concave mirrors called converging mirrors?

Answer: Concave mirrors are called converging mirrors because they converge parallel rays of light to a point called the principal focus after reflection.

Q3. Why are convex mirrors called diverging mirrors?

Answer: Convex mirrors are called diverging mirrors because they make parallel rays of light appear to diverge from the principal focus after reflection.

Q4. Why is a convex mirror used as a rear-view mirror in vehicles?

Answer: A convex mirror is used as a rear-view mirror because it always forms a virtual, erect and diminished image. It also provides a wider field of view, allowing the driver to see more area behind the vehicle.

Q5. Why is a concave mirror used by dentists?

Answer: Dentists use concave mirrors because when the object is placed between pole and focus, the mirror forms a virtual, erect and magnified image of the teeth.

Q6. Write the new Cartesian sign convention for spherical mirrors.

Answer:

• The pole of the mirror is taken as the origin.
• The principal axis is taken as the x-axis.
• Distances measured in the direction of incident light are positive.
• Distances measured opposite to the direction of incident light are negative.
• Distances measured upward from the principal axis are positive.
• Distances measured downward from the principal axis are negative.

Q7. Write mirror formula and magnification formula.

Answer:

1/f = 1/v + 1/u

m = h_i/h_o = −v/u

Here, f = focal length, v = image distance, u = object distance and m = magnification.

Q8. What happens when light travels from air to glass?

Answer: When light travels from air to glass, it enters a denser medium. Its speed decreases and the ray bends towards the normal.

Q9. What happens when light travels from glass to air?

Answer: When light travels from glass to air, it enters a rarer medium. Its speed increases and the ray bends away from the normal.

Q10. Why does a pencil appear bent when partly dipped in water?

Answer: The pencil appears bent because light rays coming from the part of the pencil inside water bend when they pass from water to air. This bending is due to refraction.

Q11. Differentiate between convex and concave lens.

Q12. Write lens formula and magnification formula for lenses.

Answer:

1/f = 1/v − 1/u

m = h_i/h_o = v/u

Q1. Explain the important terms related to spherical mirrors.

Answer:

• Pole: The centre of the reflecting surface of a spherical mirror is called pole.
• Centre of curvature: The centre of the sphere of which the mirror is a part is called centre of curvature.
• Radius of curvature: The distance between pole and centre of curvature is called radius of curvature.
• Principal axis: The straight line passing through pole and centre of curvature is called principal axis.
• Principal focus: The point on the principal axis where rays parallel to the principal axis meet or appear to meet after reflection.
• Focal length: The distance between pole and principal focus is called focal length.
• Aperture: The diameter of the reflecting surface of the mirror is called aperture.

Q2. Explain image formation by a concave mirror for different positions of object.

Q3. Explain image formation by a convex mirror.

Answer: A convex mirror always forms a virtual, erect and diminished image behind the mirror.

Q4. Write important uses of concave and convex mirrors.

Answer:

Q5. Explain Snell’s law and refractive index.

Answer: Snell’s law states that for a given pair of media, the ratio of sine of angle of incidence to sine of angle of refraction is constant.

sin i / sin r = n₂₁

This constant is called the refractive index of the second medium with respect to the first medium.

Absolute refractive index:

n = c / v

where c is speed of light in vacuum and v is speed of light in the medium.

Relative refractive index:

n₂₁ = n₂ / n₁ = v₁ / v₂

Q6. Explain the important terms related to spherical lenses.

Answer:

• Optical centre: The central point of a lens through which light passes without deviation.
• Principal axis: The straight line passing through the two centres of curvature and optical centre.
• Principal focus: The point where rays parallel to the principal axis meet or appear to meet after refraction.
• Focal length: The distance between optical centre and principal focus.
• Centre of curvature: The centre of the sphere of which the lens surface is a part.
• Aperture: The effective diameter of the circular outline of the lens.

Q7. Explain image formation by a convex lens.

Q8. Explain image formation by a concave lens.

Answer: A concave lens always forms a virtual, erect and diminished image on the same side of the lens as the object.

Q1. An object is placed 30 cm in front of a concave mirror of focal length 15 cm. Find the image distance and magnification.

Solution:

Given: u = −30 cm, f = −15 cm

1/f = 1/v + 1/u

1/−15 = 1/v + 1/−30

1/v = −1/15 + 1/30 = −1/30

v = −30 cm

m = −v/u = −(−30)/(−30) = −1

Answer: Image is formed 30 cm in front of the mirror. It is real, inverted and same size.

Q2. A concave mirror has focal length 20 cm. An object is placed 60 cm from the mirror. Find the image distance.

Solution:

Given: f = −20 cm, u = −60 cm

1/f = 1/v + 1/u

1/−20 = 1/v + 1/−60

1/v = −1/20 + 1/60 = −2/60 = −1/30

v = −30 cm

Answer: Image is formed 30 cm in front of the mirror, between F and C.

Q3. A convex mirror has focal length 25 cm. An object is placed 50 cm in front of it. Find image distance.

Solution:

Given: f = +25 cm, u = −50 cm

1/f = 1/v + 1/u

1/25 = 1/v − 1/50

1/v = 1/25 + 1/50 = 3/50

v = 50/3 = 16.67 cm

Answer: Image is formed 16.67 cm behind the mirror. It is virtual, erect and diminished.

Q4. A concave mirror forms a real image 40 cm in front of the mirror when the object is 60 cm in front. Find focal length.

Solution:

Given: u = −60 cm, v = −40 cm

1/f = 1/v + 1/u

1/f = −1/40 − 1/60 = −5/120 = −1/24

f = −24 cm

Answer: Focal length is 24 cm. Negative sign shows it is a concave mirror.

Q5. An object 4 cm high is placed 30 cm from a concave mirror of focal length 20 cm. Find image distance, magnification and image height.

Solution:

Given: h_o = +4 cm, u = −30 cm, f = −20 cm

1/−20 = 1/v + 1/−30

1/v = −1/20 + 1/30 = −1/60

v = −60 cm

m = −v/u = −(−60)/(−30) = −2

m = h_i/h_o

h_i = −2 × 4 = −8 cm

Answer: Image is formed 60 cm in front of the mirror. Image is real, inverted and 8 cm high.

Q6. A concave mirror gives a magnification of −3. If the object is placed 20 cm in front of the mirror, find image distance.

Solution:

Given: m = −3, u = −20 cm

m = −v/u

−3 = −v/(−20)

−3 = v/20

v = −60 cm

Answer: Image is formed 60 cm in front of the mirror.

Q1. Speed of light in glass is 2 × 10⁸ m/s. Find the refractive index of glass.

Solution:

Given: c = 3 × 10⁸ m/s, v = 2 × 10⁸ m/s

n = c/v

n = 3 × 10⁸ / 2 × 10⁸ = 1.5

Answer: Refractive index of glass is 1.5.

Q2. Refractive index of water is 1.33 and glass is 1.50. Find refractive index of glass with respect to water.

Solution:

n_gw = n_g / n_w

n_gw = 1.50 / 1.33 = 1.13 approximately

Answer: Refractive index of glass with respect to water is about 1.13.

Q3. Refractive index of diamond is 2.42. What is the speed of light in diamond?

Solution:

n = c/v

v = c/n = 3 × 10⁸ / 2.42

v = 1.24 × 10⁸ m/s approximately

Answer: Speed of light in diamond is about 1.24 × 10⁸ m/s.

Q4. A ray of light enters glass from air. If angle of incidence is 45° and angle of refraction is 28°, find refractive index of glass with respect to air.

Solution:

n = sin i / sin r

n = sin 45° / sin 28°

n = 0.707 / 0.469 = 1.51 approximately

Answer: Refractive index is approximately 1.51.

Q1. An object is placed 30 cm in front of a convex lens of focal length 15 cm. Find the image distance and magnification.

Solution:

Given: u = −30 cm, f = +15 cm

1/f = 1/v − 1/u

1/15 = 1/v − 1/−30

1/15 = 1/v + 1/30

1/v = 1/15 − 1/30 = 1/30

v = +30 cm

m = v/u = 30/−30 = −1

Answer: Image is formed 30 cm on the other side of the lens. It is real, inverted and same size.

Q2. A concave lens of focal length 20 cm has an object placed 30 cm in front of it. Find image distance.

Solution:

Given: f = −20 cm, u = −30 cm

1/f = 1/v − 1/u

1/−20 = 1/v − 1/−30

−1/20 = 1/v + 1/30

1/v = −1/20 − 1/30 = −5/60 = −1/12

v = −12 cm

Answer: Image is formed 12 cm on the same side as the object. It is virtual, erect and diminished.

Q3. Find the power of a convex lens of focal length 50 cm.

Solution:

Given: f = +50 cm = +0.50 m

P = 1/f

P = 1/0.50 = +2 D

Answer: Power of lens is +2 D.

Q4. Find the focal length of a lens of power −4 D.

Solution:

P = 1/f

f = 1/P = 1/−4 = −0.25 m

f = −25 cm

Answer: Focal length is −25 cm. The lens is concave.

Q5. Two lenses of power +3 D and −1 D are placed in contact. Find the total power and focal length of the combination.

Solution:

P = P₁ + P₂

P = +3 + (−1) = +2 D

f = 1/P = 1/2 = 0.5 m = 50 cm

Answer: Total power is +2 D and focal length is 50 cm.

Q6. A convex lens forms a real image twice the size of the object. If the object is placed 15 cm from the lens, find image distance and focal length.

Solution:

Given: u = −15 cm, m = −2 because image is real and inverted

m = v/u

−2 = v/−15

v = +30 cm

Using lens formula:

1/f = 1/v − 1/u

1/f = 1/30 − 1/−15 = 1/30 + 1/15 = 3/30 = 1/10

f = +10 cm

Answer: Image distance is 30 cm and focal length is 10 cm.

Q1. A 5 cm tall object is placed 20 cm from a concave mirror. The image is real and 15 cm tall. Find the image distance and focal length.

Solution:

Given: h_o = +5 cm, h_i = −15 cm, u = −20 cm

m = h_i/h_o = −15/5 = −3

m = −v/u

−3 = −v/(−20)

v = −60 cm

Using mirror formula:

1/f = 1/v + 1/u

1/f = −1/60 − 1/20 = −4/60 = −1/15

f = −15 cm

Answer: Image distance is −60 cm and focal length is −15 cm.

Q2. An object is placed 12 cm from a convex lens of focal length 8 cm. Find the position and nature of image.

Solution:

Given: u = −12 cm, f = +8 cm

1/f = 1/v − 1/u

1/8 = 1/v + 1/12

1/v = 1/8 − 1/12 = 1/24

v = +24 cm

m = v/u = 24/−12 = −2

Answer: Image is formed 24 cm on the other side of the lens. It is real, inverted and magnified two times.

Q3. A lens has focal length −0.5 m. Another lens of power +4 D is placed in contact with it. Find total power and nature of combination.

Solution:

First lens: f = −0.5 m

P₁ = 1/f = 1/−0.5 = −2 D

Second lens: P₂ = +4 D

P = P₁ + P₂ = −2 + 4 = +2 D

Answer: Total power is +2 D. The combination behaves like a convex lens.

Q4. A ray travels from medium A of refractive index 1.2 to medium B of refractive index 1.8. Find relative refractive index of B with respect to A and state whether light bends towards or away from normal.

Solution:

n_BA = n_B/n_A = 1.8/1.2 = 1.5

Since medium B has greater refractive index, it is optically denser than A.

Answer: Relative refractive index is 1.5 and light bends towards the normal.

Q1. A concave mirror can form both real and virtual images. What decides the nature of image?

Answer: The position of the object decides the nature of image. If the object is beyond focus, the image is real and inverted. If the object is between focus and pole, the image is virtual, erect and magnified.

Q2. Why does a convex mirror give wider field of view than a plane mirror?

Answer: A convex mirror diverges reflected rays and forms diminished images. Therefore, more objects from a larger area can be seen in it.

Q3. Why does a ray passing through the optical centre of a thin lens go undeviated?

Answer: Near the optical centre, the two refracting surfaces of a thin lens are nearly parallel. The deviations at the two surfaces are equal and opposite, so the ray passes undeviated.

Q4. If refractive index of a medium is high, what can you say about speed of light in it?

Answer: A higher refractive index means light travels slower in that medium because n = c/v.

Q5. Why is power of a concave lens negative?

Answer: A concave lens has negative focal length according to sign convention. Since P = 1/f, its power is also negative.

Q6. Why can a convex lens burn paper when placed in sunlight?

Answer: A convex lens converges parallel rays of sunlight at its focus. The concentration of heat energy at the focus can burn paper.

Q7. Why does a concave lens never form a real image of a real object?

Answer: A concave lens always diverges light rays. The refracted rays appear to come from a point on the same side of the lens, so the image is always virtual, erect and diminished.

Q8. A mirror produces an erect and magnified image. Identify the mirror and object position.

Answer: The mirror is a concave mirror. The object must be placed between the pole and focus.

Q9. A lens forms a virtual, erect and magnified image. Identify the lens and object position.

Answer: The lens is a convex lens. The object must be placed between the optical centre and focus.

Q10. Why is it necessary to convert focal length from centimetres to metres while calculating power?

Answer: Power is measured in dioptres and is defined as reciprocal of focal length in metres. Therefore, focal length must be converted into metres.

Q1. An object is placed between focus and pole of a concave mirror. State the nature of image formed.

Answer: The image is virtual, erect and magnified. It is formed behind the mirror.

Q2. Write two uses of concave mirrors.

Answer: Concave mirrors are used in shaving mirrors and by dentists. They are also used in torches, headlights and solar furnaces.

Q3. Why does light bend towards the normal when it enters glass from air?

Answer: Glass is optically denser than air. When light enters glass from air, its speed decreases, so it bends towards the normal.

Q4. Define one dioptre.

Answer: One dioptre is the power of a lens whose focal length is 1 metre.

1 D = 1 m⁻¹

Q5. A lens has power +5 D. Find its focal length and nature.

Answer:

f = 1/P = 1/5 = 0.2 m = 20 cm

Positive power means the lens is convex.

Q6. What is the difference between real and virtual image?

Q1. A concave mirror forms a real image twice the size of the object. If focal length is 10 cm, find the object distance.

Solution:

Real image means m = −2.

m = −v/u

−2 = −v/u, so v = 2u

For concave mirror, f = −10 cm.

1/f = 1/v + 1/u

1/−10 = 1/(2u) + 1/u = 3/(2u)

2u = −30, so u = −15 cm

Answer: Object distance is 15 cm in front of the mirror.

Q2. A ray of light passes from medium A to medium B without bending, although the media are different. Give two possible reasons.

Answer:

• The ray may be incident normally on the surface.
• The two media may have the same refractive index.

Q3. A convex lens of power +10 D is combined with a concave lens of focal length 25 cm. Find the total power.

Solution:

Convex lens: P₁ = +10 D

Concave lens: f = −25 cm = −0.25 m

P₂ = 1/f = 1/−0.25 = −4 D

P = +10 − 4 = +6 D

Answer: Total power is +6 D.

Q4. A convex lens forms an image at 60 cm when the object is placed at 20 cm. Find focal length and magnification.

Solution:

Given: u = −20 cm, v = +60 cm

1/f = 1/v − 1/u = 1/60 − 1/−20

1/f = 1/60 + 3/60 = 4/60 = 1/15

f = 15 cm

m = v/u = 60/−20 = −3

Answer: Focal length is 15 cm and magnification is −3.

Q1. Assertion: Convex mirrors are used as rear-view mirrors. Reason: Convex mirrors provide a wider field of view.

Answer: A. Both Assertion and Reason are true and Reason is the correct explanation.

Q2. Assertion: A concave mirror always forms a real image. Reason: A concave mirror is a converging mirror.

Answer: D. Assertion is false but Reason is true. A concave mirror can form a virtual image when the object is between pole and focus.

Q3. Assertion: Light bends towards the normal when it enters glass from air. Reason: Speed of light decreases in glass.

Answer: A. Both Assertion and Reason are true and Reason is the correct explanation.

Q4. Assertion: Power of concave lens is negative. Reason: Focal length of concave lens is negative according to sign convention.

Answer: A. Both Assertion and Reason are true and Reason is the correct explanation.

Q5. Assertion: A ray passing through optical centre of a thin lens goes undeviated. Reason: The optical centre is the central point of the lens.

Answer: B. Both Assertion and Reason are true but Reason is not the correct explanation.