Q. No.Consider light travelling from a medium \(A\) to medium \(B\) separated by a plane interface. If the light undergoes total internal reflection during its travel from medium \(A\) to \(B\) and the speed of light in media \(A\) and \(B\) are \(2.4\times 10^{8}~\text{m/s}\) and \(2.7\times 10^{8}~\text{m/s}\) respectively, then the value of critical angle is:
1. \(\cot ^{-1}\left(\dfrac{3}{\sqrt{13}}\right)\)
2. \(\sin ^{-1}\left(\dfrac{9}{8}\right)\)
3. \(\tan ^{-1}\left(\dfrac{8}{\sqrt{17}}\right)\)
4. \(\cos ^{-1}\left(\dfrac{8}{9}\right)\)
1. \(\cot ^{-1}\left(\dfrac{3}{\sqrt{13}}\right)\)
2. \(\sin ^{-1}\left(\dfrac{9}{8}\right)\)
3. \(\tan ^{-1}\left(\dfrac{8}{\sqrt{17}}\right)\)
4. \(\cos ^{-1}\left(\dfrac{8}{9}\right)\)
Subtopic: Total Internal Reflection |
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A transparent block \(A\) having refractive index \(μ=1.25 \) is surrounded by another medium of refractive index \(μ=1.0 \) as shown in figure. A light ray is incident on the flat face of the block with incident angle \(\theta \) as shown in figure. What is the maximum value of \(\theta \) for which light suffers total internal reflection at the top surface of the block?
1. \(\tan ^{-1}\dfrac{3}{4} \)
2. \(\cos ^{-1}\dfrac{3}{4} \)
3. \(\tan ^{-1}\dfrac{4}{3} \)
4. \(\sin ^{-1}\dfrac{3}{4} \)
1. \(\tan ^{-1}\dfrac{3}{4} \)
2. \(\cos ^{-1}\dfrac{3}{4} \)
3. \(\tan ^{-1}\dfrac{4}{3} \)
4. \(\sin ^{-1}\dfrac{3}{4} \)
Subtopic: Total Internal Reflection |
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Level 3: 35%-60%
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At the interface between two materials having refractive indices \({n}_1\) and \({n}_2\), the critical angle for reflection of an electromagnetic wave is \(\theta_{1c} \). The \({n}_2\) material is replaced by another material having refractive index \({n}_3\) such that the critical angle at the interface between \({n}_1\) and \({n}_3\) materials is \(\theta_{2c}\). If \({n}_3>{n}_2>{n}_1 \); \(n_2 / n_3=2 / 5 \) and \(\sin \theta_{2 c}-\sin \theta_{1 c}=1 / 2 \) then \(\theta_{1c}\) is:
1. \(\sin ^{-1}\left(\dfrac{5}{6 n_1}\right) \)
2. \(\sin ^{-1}\left(\dfrac{2}{3 n_1}\right) \)
3. \(\sin ^{-1}\left(\dfrac{1}{3 n_1}\right) \)
4. none of these
1. \(\sin ^{-1}\left(\dfrac{5}{6 n_1}\right) \)
2. \(\sin ^{-1}\left(\dfrac{2}{3 n_1}\right) \)
3. \(\sin ^{-1}\left(\dfrac{1}{3 n_1}\right) \)
4. none of these
Subtopic: Total Internal Reflection |
Level 4: Below 35%
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Critical angle of incidence for a pair of optical media is \(45^\circ .\) The refractive indices of first and second media are in the ratio:
1. \(1:\sqrt{2}\)
2. \(1:2\)
3. \(\sqrt{2}:1\)
4. \(2:1\)
1. \(1:\sqrt{2}\)
2. \(1:2\)
3. \(\sqrt{2}:1\)
4. \(2:1\)
Subtopic: Total Internal Reflection |
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If light is passing through a medium of critical angle \(45^o\), then the wave speed will be
1. \({3 \over \sqrt 2 } \times 10^8~ m/s\)
2. \(3 \sqrt 2 \times 10^8 ~m/s\)
3. \({3 \over 2} \times 10^8 ~m/s\)
4. \(3 \times 10^8~ m/s\)
1. \({3 \over \sqrt 2 } \times 10^8~ m/s\)
2. \(3 \sqrt 2 \times 10^8 ~m/s\)
3. \({3 \over 2} \times 10^8 ~m/s\)
4. \(3 \times 10^8~ m/s\)
Subtopic: Total Internal Reflection |
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Level 1: 80%+
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A light wave travelling linearly in a medium of dielectric constant 4, incident on the horizontal interface separating medium with air. The angle of incidence for which the total intensity of the incident wave will be reflected back into the same medium will be: (Given: relative permeability of medium \(\mu_r = 1\))
1. 10°
2. 20°
3. 30°
4. 60°
1. 10°
2. 20°
3. 30°
4. 60°
Subtopic: Total Internal Reflection |
Level 3: 35%-60%
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The speed of light in media 'A' and 'B' are 2.0 × 1010 cm/s and 1.5 × 1010 chm/s respectively. A ray of light enters from the medium B to A at an incident angle '\(\theta\)'. If the ray suffers total internal reflection, then
1. \(\theta=\sin ^{-1}\left(\frac{3}{4}\right) \)
2. \(\theta>\sin ^{-1}\left(\frac{2}{3}\right) \)
3. \(\theta<\sin ^{-1}\left(\frac{3}{4}\right) \)
4. \(\theta>\sin ^{-1}\left(\frac{3}{4}\right)\)
1. \(\theta=\sin ^{-1}\left(\frac{3}{4}\right) \)
2. \(\theta>\sin ^{-1}\left(\frac{2}{3}\right) \)
3. \(\theta<\sin ^{-1}\left(\frac{3}{4}\right) \)
4. \(\theta>\sin ^{-1}\left(\frac{3}{4}\right)\)
Subtopic: Total Internal Reflection |
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Light travels in two media \(M_1\) and \(M_2\) with speeds \(1.5 \times 10^8 ~\text{ms}^{-1}\) and \(2.0 \times 10^8~ \text{ms}^{-1}\) respectively. The critical angle between them is:
1. \( \tan ^{-1}\left(\dfrac{3}{\sqrt{7}}\right ) \)
2. \( \tan ^{-1}\left(\dfrac{2}{3}\right) \)
3. \(\cos ^{-1}\left(\dfrac{3}{4}\right) \)
4. \(\sin ^{-1}\left(\dfrac{2}{3}\right)\)
1. \( \tan ^{-1}\left(\dfrac{3}{\sqrt{7}}\right ) \)
2. \( \tan ^{-1}\left(\dfrac{2}{3}\right) \)
3. \(\cos ^{-1}\left(\dfrac{3}{4}\right) \)
4. \(\sin ^{-1}\left(\dfrac{2}{3}\right)\)
Subtopic: Total Internal Reflection |
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A ray of light entering from air into a denser medium of refractive index \({4\over 3},\) as shown in the figure. The light ray suffers total internal reflection at the adjacent surface as shown below. The maximum value of angle should be equal to:
1. \({\sin^{-1}{\sqrt{5}\over 4}}\)
2. \({\sin^{-1}{\sqrt{7}\over 3}}\)
3. \({\sin^{-1}{\sqrt{7}\over 4}}\)
4. \({\sin^{-1}{\sqrt{5}\over 3}}\)
1. \({\sin^{-1}{\sqrt{5}\over 4}}\)
2. \({\sin^{-1}{\sqrt{7}\over 3}}\)
3. \({\sin^{-1}{\sqrt{7}\over 4}}\)
4. \({\sin^{-1}{\sqrt{5}\over 3}}\)
Subtopic: Total Internal Reflection |
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A ray of laser of a wavelength \(630~ \text{nm}\) is incident at an angle of \({30^\circ}\) at the diamond-air interface. It is going from diamond to air. The refractive index diamond is \(2.42\) and that of air is \(1.\) Choose the correct option.
| 1. | the angle of refraction is \(53.4^\circ\) |
| 2. | the angle of refraction is \(\mathrm{30^\circ}\) |
| 3. | the angle of refraction is \(24.41^\circ\) |
| 4. | refraction is not possible |
Subtopic: Total Internal Reflection |
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Level 2: 60%+
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