SATHEE: Ray Optics and Optical Instruments

Ray Optics and Optical Instruments - Result Question 18

18. Light enters at an angle of incidence in a transparent rod of refractive index $n$ . For what value of the refractive index of the material of the rod the light once entered into it will not leave it through its lateral face whatsoever be the value of angle of incidence?

[1998]

(a) $n > \sqrt{2}$

(b) $n = 1$

(d) $n = 1.3$

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Answer:

Correct Answer: 18. (a)

Solution:

(a) Let a ray of light enter at $A$ and the refracted beam is $A B$ . This is incident at an angle $θ$ . For no refraction at the lateral face, $θ > C$

or, $\sin θ > \sin C$ But $θ + r = 90^{\circ} \Rightarrow θ = (90^{\circ} - r)$

$∴ \sin (90^{\circ} - r) > \sin C$

or $\cos r > \sin C$

From Snell’s law, $n = \frac{\sin i}{\sin r} \Rightarrow \sin r = \frac{\sin i}{n}$

$∴ \cos r = \sqrt{1 - \sin^{2} r} = \sqrt{(1 - \frac{\sin^{2} i}{n^{2}})}$

$∴$ equation (1) gives

$\sqrt{1 - \frac{\sin^{2} i}{n^{2}}} > \sin C \Rightarrow 1 - \frac{\sin^{2} i}{n^{2}} > \sin^{2} C$

Also, $\sin C = \frac{1}{n}$

$∴ 1 - \frac{\sin^{2} i}{n^{2}} > \frac{1}{n^{2}}$ or $1 > \frac{\sin^{2} i}{n^{2}} + \frac{1}{n^{2}}$

or $\frac{1}{n^{2}} (\sin^{2} i + 1) < 1$ or $n^{2} > (\sin^{2} i + 1)$

Maximum value of $\sin i = 1$

$∴ n^{2} > 2 \Rightarrow n > \sqrt{2}$

Ray Optics and Optical Instruments - Result Question 18

18. Light enters at an angle of incidence in a transparent rod of refractive index $n$ . For what value of the refractive index of the material of the rod the light once entered into it will not leave it through its lateral face whatsoever be the value of angle of incidence?

Answer:

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Ray Optics and Optical Instruments - Result Question 18

18. Light enters at an angle of incidence in a transparent rod of refractive index n. For what value of the refractive index of the material of the rod the light once entered into it will not leave it through its lateral face whatsoever be the value of angle of incidence?

Answer:

Engineering Preparation

Medical Preparation

NCERT Books & Solutions

Important Resources

Other Resources

Syllabus

Test Platform

Sample Mock Test

Mentorship

NCERT Exercise Video Solution

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18. Light enters at an angle of incidence in a transparent rod of refractive index $n$ . For what value of the refractive index of the material of the rod the light once entered into it will not leave it through its lateral face whatsoever be the value of angle of incidence?