JEE Advanced 2013 · Paper 2 · Physics Q18

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PhysicsList match+3 / -1Question 18 of 60

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:

A rectangular block (index μ₂) in a medium μ₃ contains a right-angled isosceles prism (index μ₁) with its vertical face on the left and hypotenuse faces at 45°. Ray e enters horizontally from the left, crosses the vertical face and meets the upper slanted face at 45°: it can leave bent upward (f), straight (g), bent downward (h), or be totally reflected down to the lower slanted face and back out to the left as ray i.

List I

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

List II

1
$\mu_1>\sqrt2\,\mu_2$
2
$\mu_2>\mu_1$ and $\mu_2>\mu_3$
3
$\mu_1=\mu_2$
4
$\mu_2<\mu_1<\sqrt2\,\mu_2$ and $\mu_2>\mu_3$

P → 2; Q → 3; R → 1; S → 4

P → 1; Q → 2; R → 4; S → 3

P → 4; Q → 1; R → 2; S → 3

P → 2; Q → 3; R → 4; S → 1

Answer and worked solution

Official answer: D

At the slanted face the ray inside the prism (index $\mu_1$ ) meets the boundary with $\mu_2$ at 45°.

$e\to f$ (bends away from the normal toward the upper side): passes into a denser block, $\mu_2>\mu_1$ , and then leaves into $\mu_3$ with $\mu_2>\mu_3$ . → 2
$e\to g$ (undeviated): $\mu_1=\mu_2$ . → 3
$e\to h$ (bends the other way, no total reflection): $\mu_2<\mu_1<\sqrt2\mu_2$ (so $\sin45°<\mu_2/\mu_1$ ), with $\mu_2>\mu_3$ . → 4
$e\to i$ (totally reflected twice and sent back): $\sin45°>\frac{\mu_2}{\mu_1}$ , i.e. $\mu_1>\sqrt2\mu_2$ . → 1

Code 2 3 4 1.

(D)

Topics:Total internal reflection Refraction at plane surfaces

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JEE Advanced 2013 · Paper 2, Physics question 18