A monochromatic light wave is incident normally on a glass slab of thickness $d$ , as shown in the figure. The refractive index of the slab increases linearly from $n_{1}$ to $n_{2}$ over the height $h$ . Which of the following statement(s) is(are) true about the light wave emerging out of the slab [2023]

Question

Smart Achievers · Accepted Answer

(2, 4)

From the figure, $n_{1} d + ℓ = n_{2} d$

$∴$ $ℓ = n_{2} d - n_{1} d = (n_{2} - n_{1}) d$

$∴$ $\tan θ = \frac{ℓ}{h} = \frac{(n_{2} - n_{1}) d}{h}$

$∴$ Light wave emerging out of the slab is deflected by an angle $θ = \tan^{- 1} [\frac{(n_{2} - n_{1}) d}{h}]$

It depends only on $(n_{2} - n_{1})$ and not on the individual values of $n_{1}$ and $n_{2}$ .

Solution

1 It will deflect up by an angle $\tan^{- 1} [\frac{(n_{2}^{2} - n_{1}^{2}) d}{2 h}] .$

2 It will deflect up by an angle $\tan^{- 1} [\frac{(n_{2} - n_{1}) d}{h}] .$

3 It will not deflect.

4 The deflection angle depends only on $(n_{2} - n_{1})$ and not on the individual values of $n_{1}$ and $n_{2}$ .

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Solution

Q. A monochromatic light wave is incident normally on a glass slab of thickness d, as shown in the figure. The refractive index of the slab increases linearly from n1 to n2 over the height h. Which of the following statement(s) is(are) true about the light wave emerging out of the slab [2023]

1 It will deflect up by an angle tan-1[(n22-n12)d2h].

2 It will deflect up by an angle tan-1[(n2-n1)dh].

3 It will not deflect.

4 The deflection angle depends only on (n2-n1) and not on the individual values of n1 and n2.

Ans. (2, 4) From the figure, n1d+ℓ=n2d ∴ ℓ=n2d-n1d=(n2-n1)d ∴ tanθ=ℓh=(n2-n1)dh ∴ Light wave emerging out of the slab is deflected by an angle θ=tan-1[(n2-n1)dh] It depends only on (n2-n1) and not on the individual values of n1 and n2.

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1 It will deflect up by an angle $\tan^{- 1} [\frac{(n_{2}^{2} - n_{1}^{2}) d}{2 h}] .$

2 It will deflect up by an angle $\tan^{- 1} [\frac{(n_{2} - n_{1}) d}{h}] .$

4 The deflection angle depends only on $(n_{2} - n_{1})$ and not on the individual values of $n_{1}$ and $n_{2}$ .