A transparent slab of thickness has a refractive index that increases with . Here is the vertical distance inside the slab, measured from the top. The slab is placed between two media with uniform refractive indices and , as shown in the figure. [20

Question

A transparent slab of thickness $d$ has a refractive index $n (z)$ that increases with $z$ . Here $z$ is the vertical distance inside the slab, measured from the top. The slab is placed between two media with uniform refractive indices $n_{1}$ and $n_{2}$ $(n_{2} > n_{1})$ , as shown in the figure. A ray of light is incident with an angle $θ_{i}$ from medium 1 and emerges in medium 2 with refraction angle $θ_{t}$ with a lateral displacement $l$ . [2016]

Which of the following statement(s) is(are) true

Which of the following statement(s) is(are) true?

Smart Achievers · Accepted Answer

(1, 3, 4)

From Snell's law, $n (z)$ $[∵ interfaces 1 and 2 are parallel]$

$l$ depends on the refractive index of transparent slab $n (z)$ but not on $n_{2}$ . But $θ_{f}$ depends on $n_{2}$ .

Because lateral displacement $(l)$ is possible due to $μ$ of slab and angle of incidence $θ_{i}$ .

Solution

1 $n_{1} \sin θ_{i} = n_{2} \sin θ_{f}$

2 $n_{1} \sin θ_{i} = (n_{2} - n_{1}) \sin θ_{f}$

3 $l$ is independent of $n_{2}$

4 $l$ is dependent on $n (z)$

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Solution

1 n1sinθi=n2sinθf

2 n1sinθi=(n2-n1)sinθf

3 l is independent of n2

4 l is dependent on n(z)

Ans. (1, 3, 4) From Snell's law, n1sinθi=n2sinθf [∵interfaces 1 and 2 are parallel] l depends on the refractive index of transparent slab n(z) but not on n2. But θf depends on n2. Because lateral displacement (l) is possible due to μ of slab and angle of incidence θi.

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1 $n_{1} \sin θ_{i} = n_{2} \sin θ_{f}$

2 $n_{1} \sin θ_{i} = (n_{2} - n_{1}) \sin θ_{f}$

3 $l$ is independent of $n_{2}$

4 $l$ is dependent on $n (z)$