A right angled prism of refractive index $\mu_{1}$ is placed in a rectangular block of refractive index $\mu_{2}$, which is surrounded by a medium of refractive index $\mu_{3}$, as shown in the figure. A ray of light 'e' enters the rectangular block at normal incidence. Depending upon the relationships between $\mu_{1}, \mu_{2}$ and $\mu_{3}$, it takes one of the four possible paths 'ef', 'eg', 'eh' or 'ei'. Match the paths in List I with conditions of refractive indices in List II and select the correct answer using the codes given below the lists: | List I | | | --- | --- | | P. | $e \rightarrow f$ | | Q. | $e \rightarrow g$ | | R. | $e \rightarrow h$ | | S. | $e \rightarrow i$ | | List II | | | --- | --- | | 1. | $\mu_{1}>\sqrt{2} \mu_{2}$ | | 2. | $\mu_{2}>\mu_{1}$ and $\mu_{2}>\mu_{3}$ | | 3. | $\mu_{1}=\mu_{2}$ | | 4. | $\mu_{2} \mu_{3}$ | Codes :

JEE Advanced · 2013 · 02 Jun 2013 · Paper 2 · Geometrical Optics

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 in List II and select the correct answer using the codes given below the lists:

List I
P.	$e \to f$
Q.	$e \to g$
R.	$e \to h$
S.	$e \to i$

List II
1.	$μ_{1} > 2 μ_{2}$
2.	$μ_{2} > μ_{1}$ and $μ_{2} > μ_{3}$
3.	$μ_{1} = μ_{2}$
4.	$μ_{2} < μ_{1} < 2 μ_{2}$ and $μ_{2} > μ_{3}$

Codes :

(A)P-2, Q-3, R-1, S-4
(B)P-1, Q-2, R-4, S-3
(C)P-4, Q-1, R-2, S-3
(D)P-2, Q-3, R-4, S-1✓ Correct

Answer: (D)

Solution

Path e→f: Ray refracts into the prism and then out. This requires

μ_{2} > μ_{1}

(refraction into denser to rarer at prism interface) and

μ_{2} > μ_{3}

(refraction out of block). → 2

Path e→g: Ray passes straight through without bending at prism interface. This requires

μ_{1} = μ_{2}

. → 3

Path e→h: Ray undergoes partial TIR at prism interface (critical angle > 45°). This requires

sin θ_{C} > sin 45°

, so

\frac{μ _{2}}{μ _{1}} > \frac{1}{2}

, giving

μ_{2} < μ_{1} < 2 μ_{2}

. → 4

Path e→i: Ray undergoes complete TIR at prism interface (critical angle < 45°). This requires

μ_{1} > 2 μ_{2}

. → 1

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

JEE Advanced · 2013 · 02 Jun 2013 · Paper 2 · Single correct option

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JEE Advanced · 2013 · 02 Jun 2013 · Paper 2 · Geometrical Optics

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