A right angled prism of refractive index is placed in a rectangular block of refractive index , which is surrounded by a medium of refractive index , as shown in the figure. A ray of light enters the rectangular block at normal incidence. [2013]

Question

A right angled prism of refractive index $μ_{1}$ is placed in a rectangular block of refractive index $μ_{2}$ , which is surrounded by a medium of refractive index $μ_{3}$ , as shown in the figure. A ray of light $' e'$ enters the rectangular block at normal incidence. Depending upon the relationships between $μ_{1}$ , $μ_{2}$ and $μ_{3}$ , it takes one of the four possible paths 'ef', 'eg', 'eh' or 'ei'.

Match the paths in List I with conditions of refractive indices given in List II and select the correct answer using the codes given below the lists. [2013]

	List I		List II
P.	$e \to f$	1.	$μ_{1} > \sqrt{2} μ_{2}$
Q.	$e \to g$	2.	$μ_{2} > μ_{1} and μ_{2} > μ_{3}$
R.	$e \to h$	3.	$μ_{1} = μ_{2}$
S.	$e \to i$	4.	$μ_{2} < μ_{1} < \sqrt{2} μ_{2} and μ_{2} > μ_{3}$

Codes:

Smart Achievers · Accepted Answer

(4)

$e \to f$

When the ray enters from the rectangular block to prism, the angle of incidence is greater than the angle of refraction. Hence, $μ_{2} > μ_{1} .$ The ray then moves away from the normal when it emerges out of the rectangular block. Therefore, $μ_{1}$

$e \to g$

As there is no deviation of the ray as it emerges out of the prism, $∴$ $μ_{2} = μ_{1} .$

$e \to h$

As the ray emerges out of the prism, it moves away from the normal. $∴$ $μ_{2} < μ_{1} .$ The ray moves away from the normal as it emerges out of the rectangular block. $∴$ $μ_{2} > μ_{3} .$

$e \to i$

At the prism surface, total internal reflection has taken place.

$∴$ $Critical angle 45 ° > C$ $\Rightarrow \sin 45 ° > \sin C$

$μ_{1} = μ_{2}$ $∴$ $μ_{1} > \sqrt{2} μ_{2}$

Solution

1 P-2, Q-3, R-1, S-4

2 P-1, Q-2, R-4, S-3

3 P-4, Q-1, R-2, S-3

4 P-2, Q-3, R-4, S-1

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