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The adjacent diagram represents a glass slab of refractive index 1.5. If PA, PB, PC and PD represent the rays of light from a point P at the bottom of the block, draw the approximate directions of these rays as they emerge out of the glass slab. (sin 42° = 2/3)

The adjacent diagram represents a glass slab of refractive index 1.5. If PA, PB, PC and PD represent the rays of light from a point P at the bottom of the block, draw the approximate directions of these rays as they emerge out of the glass slab. Concise Physics Solutions ICSE Class 10.

Refraction Plane Surfaces

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Answer

Given,

Refractive index of glass with respect to air = aμg = 1.5 = 1gμa\dfrac{1}{\text g\text μ\text a}

Angle made by PA with normal = 0°

Angle made by PB with normal = 30°

Angle made by PC with normal = 42°

Angle made by PD with normal = 60°

sin 42° = 2/3

The adjacent diagram represents a glass slab of refractive index 1.5. If PA, PB, PC and PD represent the rays of light from a point P at the bottom of the block, draw the approximate directions of these rays as they emerge out of the glass slab. Concise Physics Solutions ICSE Class 10.

(i) For ray PA

i = 0°

sin r=sin igμa=sin 0°×1.5=0\text {sin r} = \dfrac{\text{sin i}}{{g\text{μ}a}}=\text {sin }0°\times 1.5 =0

⟹ r = sin-1(0) = 0°

Ray PA will not deviate and emerge straight.

(ii) For PB

i = 30°

sin r=sin igμa=sin 30°×1.5=0.5×1.5=0.75\text {sin r} = \dfrac{\text{sin i}}{{\text{g}\text{μ}a}}=\text {sin}\ 30°\times 1.5 = 0.5\times1.5=0.75

⟹ r = sin-1(0.75) ≈ 49°

Ray PB will emerge at an angle of 49° with the normal.

(iii) For PC

i = 42°

sin r=sin igμa=sin 42°×1.5=23×1.5=1\text {sin r} = \dfrac{\text{sin i}}{{\text{g}\text{μ}a}}=\text {sin}\ 42°\times 1.5 = \dfrac{2}{3} \times1.5=1

⟹ r = sin-1(1) = 90°

This is the condition for critical angle.

Ray PC will graze along the surface.

(iv) For PD

i = 60°

sin r=sin igμa=sin 60°×1.5=32×1.5≈1.3\text {sin r} = \dfrac{\text{sin i}}{{\text {g}\text{μ}a}}=\text {sin}\ 60°\times 1.5 = \dfrac{\sqrt 3}{2} \times1.5≈1.3

Here,

sin r > 1 which a condition of total internal reflection.

Ray PD will suffer total internal reflection.

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