Q. No.Light ray incident along a vector \(\overrightarrow{A O}~(\overrightarrow{A O}=2 \hat{i}-3 \hat{j})\) emerges out along vector \(\overrightarrow{O B}~(\overrightarrow{O B}=C \hat{i}-4 \hat{j})\) as shown in the figure below. The value of \(C\) is:
1. \(1.6\)
2. \(0.16\)
3. \(11.6\)
4. \(16\)
1. \(1.6\)
2. \(0.16\)
3. \(11.6\)
4. \(16\)
Subtopic: Refraction at Plane Surface |
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The wavelength of light, while it is passing through water is \(540~\text{nm}.\) The refractive index of water is \(\dfrac{4}{3}.\) The wavelength of the same light when it is passing through a transparent medium having refractive index of \(\dfrac{3}{2}\) is: (in nm)
1. \(380\)
2. \(840\)
3. \(480\)
4. \(540\)
1. \(380\)
2. \(840\)
3. \(480\)
4. \(540\)
Subtopic: Refraction at Plane Surface |
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Given below are two statements:
In the light of the above statements, choose the most appropriate answer from the options given below:
| Assertion (A): | Refractive index of glass is higher than that of air. |
| Reason (R): | Optical density of a medium is directly proportional to its mass density which results in a proportionate refractive index. |
| 1. | Both (A) and (R) are True and (R) is the correct explanation of (A). |
| 2. | Both (A) and (R) are True but (R) is not the correct explanation of (A). |
| 3. | (A) is True but (R) is False. |
| 4. | (A) is False but (R) is True. |
Subtopic: Refraction at Plane Surface |
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A container contains a liquid with refractive index \(1.2\) up to a height of \(60~\text{cm}\) and another liquid having refractive index \(1.6\) is added to height \(H\) above first liquid. If viewed from above, the apparent shift in the position of bottom of container is \(40~\text{cm}.\) The value of \(H\) is:
1. \(60~\text{cm} \)
2. \(80~\text{cm} \)
3. \(70~\text{cm} \)
4. \(50~\text{cm} \)
1. \(60~\text{cm} \)
2. \(80~\text{cm} \)
3. \(70~\text{cm} \)
4. \(50~\text{cm} \)
Subtopic: Refraction at Plane Surface |
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The refractive index of the material of a glass prism is \(\sqrt 3.\) The angle of minimum deviation is equal to the angle of the prism. What is the angle of the prism?
1. \(58^\circ\)
2. \(48^\circ\)
3. \(60^\circ\)
4. \(50^\circ\)
1. \(58^\circ\)
2. \(48^\circ\)
3. \(60^\circ\)
4. \(50^\circ\)
Subtopic: Refraction at Plane Surface |
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What is the lateral shift of a ray refracted through a parallel-sided glass slab of thickness \(h\) in terms of the angle of incidence \(i\) and angle of refraction \(r,\) if the glass slab is placed in air medium?
1. \(\dfrac{h \tan (i-r)}{\tan r}\)
2. \(\dfrac{h \cos (i-r)}{\sin r}\)
3. \(\dfrac{h \sin (i-r)}{\cos r}\)
4. \(h\)
1. \(\dfrac{h \tan (i-r)}{\tan r}\)
2. \(\dfrac{h \cos (i-r)}{\sin r}\)
3. \(\dfrac{h \sin (i-r)}{\cos r}\)
4. \(h\)
Subtopic: Refraction at Plane Surface |
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Two light beams fall on a transparent material block at point \(1\) and \(2\) with angle \(\theta_1\) and \(\theta_2\) respectively, as shown in figure.
After refraction, the beams intersect at point \(3\) which is exactly on the interface at other end of the block.
The distance between \(1\) and \(2 \) is \(d=4 \sqrt{3} \) cm and \(\theta_1=\theta_2=\cos ^{-1}\left(n_2 /\left(2 n_1\right)\right. \), where refractive index of the block \(n_2 > \) refractive index of the outside medium \(n_1 \), then the thickness of the block is: (in cm)
1. \(2\)
2. \(4\)
3. \(3\)
4. \(6\)
After refraction, the beams intersect at point \(3\) which is exactly on the interface at other end of the block.
The distance between \(1\) and \(2 \) is \(d=4 \sqrt{3} \) cm and \(\theta_1=\theta_2=\cos ^{-1}\left(n_2 /\left(2 n_1\right)\right. \), where refractive index of the block \(n_2 > \) refractive index of the outside medium \(n_1 \), then the thickness of the block is: (in cm)
1. \(2\)
2. \(4\)
3. \(3\)
4. \(6\)
Subtopic: Refraction at Plane Surface |
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A transparent film of refractive index,\(2.0\) is coated on a glass slab of refractive index, \(1.45\). What is the minimum thickness of transparent film to be coated for the maximum transmission of Green light of wavelength \(550~\text {nm}\)? [Assume that the light is incident nearly perpendicular to the glass surface.]
1. \(94.8 ~\text {nm}\)
2. \(275~\text {nm}\)
3. \(68.7 ~\text {nm}\)
4. \(137.5 ~\text {nm}\)
1. \(94.8 ~\text {nm}\)
2. \(275~\text {nm}\)
3. \(68.7 ~\text {nm}\)
4. \(137.5 ~\text {nm}\)
Subtopic: Refraction at Plane Surface |
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A light ray is incident on a glass slab of thickness \(4 \sqrt{3}~\text{cm}\) and refractive index \(\sqrt{2}. \)The angle of incidence is equal to the critical angle for the glass slab with air. The lateral displacement of the ray after passing through the glass slab is: (Given \(\sin 15^{\circ}=0.25)\)
1. \(2~\text{cm}\)
2. \(4~\text{cm}\)
3. \(6~\text{cm}\)
4. \(8~\text{cm}\)
1. \(2~\text{cm}\)
2. \(4~\text{cm}\)
3. \(6~\text{cm}\)
4. \(8~\text{cm}\)
Subtopic: Refraction at Plane Surface |
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Two slabs of the same thickness of \(6~\text{cm}\) each are placed over one another as shown in the table.
The apparent depth of the table surface is \(N~\text{cm}.\) Then the value of \(N\) is: (\(N\) is the nearest integer)
1. \(6\)
2. \(7\)
3. \(9\)
4. \(3\)
The apparent depth of the table surface is \(N~\text{cm}.\) Then the value of \(N\) is: (\(N\) is the nearest integer)
1. \(6\)
2. \(7\)
3. \(9\)
4. \(3\)
Subtopic: Refraction at Plane Surface |
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