CG Board Class 10 Science Chapter 10 Solutions: Light: Reflection and Refraction from Plane Surface (प्रकाश: परावर्तन तथा अपवर्तन समतल सतह से) (2026-27)

(i) If we rotate a plane mirror by 2θ, then the reflected ray will rotate by:**

• (a) 2θ
• (b) 3θ
• (c) 4θ
• (d) θ

(c) 4θ

Explanation: Rotating a plane mirror by an angle α rotates the reflected ray by 2α. Therefore, rotating the mirror by 2θ rotates the reflected ray by 2 × (2θ) = 4θ.

Answer: (d) One half of the person’s height

Explanation: By the laws of reflection, light rays from head and foot require a mirror height equal to half the total height of the person.

Answer: (c) 7

Explanation: Number of images n = (360°)/(θ) – 1 = (360°)/(45°) – 1 = 8 – 1 = 7.

Answer: (b) 6 cm

Explanation: Distance of image behind mirror = 3 cm. Total distance = 3 cm + 3 cm = 6 cm.

(i) Image formed by a plane mirror is erect, virtual and ……………………**

(ii) Second law of refraction is also known as ……………………

(iii) Light ray falls normally on plane mirror; the angle of reflection will be ……………………

(iv) For …………………… light should travel from denser medium to rarer medium.

• (i) equal to the size of the object / body
• (ii) Snell’s law
• (iii) Zero (0°)
• (iv) Total Internal Reflection

1. First Law: The angle of incidence (∠ i) is always equal to the angle of reflection (∠ r).

∠ i = ∠ r

1. Second Law: The incident ray, the reflected ray, and the normal to the surface at the point of incidence all lie in the same plane.

1. First Law: The incident ray, the refracted ray, and the normal to the interface at the point of incidence all lie in the same plane.
2. Second Law (Snell’s Law): The ratio of the sine of the angle of incidence (sin i) to the sine of the angle of refraction (sin r) is constant for a given pair of media

(sin i)/(sin r) = n₂₁ = Constant

Total internal reflection can only occur when light travels from an optically denser medium to a rarer medium. Since n_A > n_B, Medium A is denser than Medium B. Therefore, total internal reflection is possible when light travels from Medium A to Medium B.

Definition: When a ray of light travelling from an optically denser medium to a rarer medium is incident at an angle greater than the critical angle, the light ray is completely reflected back into the denser medium. This phenomenon is called Total Internal Reflection**.

• Necessary Conditions:

1. Light must travel from an optically denser medium to a rarer medium.
2. The angle of incidence in the denser medium must be greater than the critical angle (∠ i > θ_c).

1. A straight stick or pencil partially immersed in water appears bent at the water surface.
2. A coin placed at the bottom of a water-filled vessel appears raised above its actual position.

The critical angle (θ_c or i_c) is defined as the specific angle of incidence in an optically denser medium for which the corresponding angle of refraction in the rarer medium is 90°(∠ r = 90°).

Given:** c = 3 × 10⁸ m/s, Refractive index of glass n_g = 1.50.

• Formula: n_g = c/v_g ⇒ v_g = c/n_g
• Calculation:

v_g = (3 × 10⁸)/(1.50) = 2 × 10⁸ m/s

The statement that the refractive index of diamond is 2.42 means that the ratio of the speed of light in vacuum to the speed of light in diamond is 2.42. In other words, light travels 2.42 times slower in diamond than in vacuum (v_diamond = (c)/(2.42) ≈ 1.24 × 10⁸ m/s).

The light ray will bend towards the normal. This is because ice is an optically denser medium (n = 1.31) compared to air (n = 1.0003). When light travels from an optically rarer medium to a denser medium, its speed decreases, causing it to bend towards the normal line.

If the distance between the mirror and the object (d_o) is increased by x, the distance between the image and the mirror (d_i) also increases by x. Consequently, the total distance between the object and the image (d_o + d_i = 2d_o) will increase by 2x (double the distance).

Absolute Refractive Index (n):** Ratio of speed of light in vacuum (c) to speed of light in that medium (v): n = c / v.

• Relative Refractive Index (n₂₁): Ratio of speed of light in Medium 1 (v₁) to speed of light in Medium 2 (v₂): n₂₁ = v₁ / v₂.
• Relation: The relative refractive index of Medium 2 with respect to Medium 1 is equal to the ratio of absolute refractive index of Medium 2 to that of Medium 1

n₂₁ = n₂/n₁

The Principle of Reversibility states that if the path of a light ray travelling through multiple media is reversed at any point, the ray retraces its entire path in the exact opposite direction.

Mathematically: {}_1n₂ × {}_2n₁ = 1 ⇒ {}_1n₂ = frac{1}{{}_2n₁}

(i) The position of a fish in a pond is not the same as it is observed from outside.**

(ii) An air bubble shines in water.

(iii) Mirage is an illusion.

(i)

(iii)

• (i) Light rays from the fish travel from water (denser) to air (rarer) and bend away from the normal. When these rays enter the eye, they form a raised virtual image, making the fish appear shallower than its actual depth.
• (ii) Light travelling in water enters the air inside the bubble at an angle greater than the critical angle for water-air interface (48.6°), undergoing Total Internal Reflection and making the bubble shine like silver.
• (iii) On hot days, ground air gets heated and rarer while upper air remains dense. Light from distant objects continuously refracts and undergoes Total Internal Reflection from hot ground air, forming an inverted virtual image that creates the illusion of water.
• (i) ,
• (ii) (48.6°) ,
• (iii) ,

Let H be the head, E be the eye, and F be the feet of a person of height HF. Light from head H reflects at point P into eye E, and light from feet F reflects at point Q into eye E.

1. Normal PR bisects HE: RE = 1/2 HE.
2. Normal QS bisects EF: ES = 1/2 EF.
3. Total required mirror length PQ

PQ = RS = RE + ES = 1/2 HE + 1/2 EF = 1/2 (HE + EF) = 1/2 HF

Thus, the minimum mirror length PQ = 1/2 × Height of person.

Refraction:** The bending of a light ray from its straight path when it passes obliquely from one transparent medium to another due to change in speed.

• Difference:
• Reflection: Light bounces back into the same medium from a polished surface without changing speed.
• Refraction: Light passes into a second transparent medium with a change in speed and direction.

Given:** n_g = 3/2, n_w = 5/4.

• Speed of light in water v_w = c/n_w, Speed of light in glass v_g = c/n_g.
• Ratio of speed of light in water to glass:

v_w/v_g = (c / n_w)/(c / n_g) = n_g/n_w = 3/2/5/4 = 3/2 × 4/5 = 12/10 = 1.2

Given:** Apparent depth (h) = 75 cm, Refractive index of water (n) = 1.33 = 4/3.

• Formula:

n = (Actual Depth (H))/(Apparent Depth (h))

• Calculation:

H = n × h = 1.33 × 75 = 4/3 × 75 = 100 cm