Expression for Apparent Depth

Q.

A coin is placed at the bottom of a beaker containing water (refractive index = $\frac{4}{3}$) to a depth of 12 cm. By what height the coin appears to be raised when seen from vertically above?

Q.

How is the refractive index of a medium related to the real and apparent depths of an object in that medium?

Q.

Water in a pond appears to be only three-quarter of its actual depth. (a) What property of light is responsible for this observation? Illustrate your answer with the help of a ray diagram. (b) How the refractive index of water calculated from its real and apparent depths?

Q.

Prove that

Refractive index = $\frac{realdepth}{apparentdepth}$

Q.

A coin placed at the bottom of a beaker appears to be raised by $4\mathrm{cm}$. If the refractive index of water is $\frac{4}{3}$, then find the depth of the water in the beaker.

Q.

An equilateral prism deviates a ray through $45°$ for the two angles of incidence differing by $20°$. What is the angle of incidence?

Q. Light is incident from air on oil at an angle of ${30}^{\circ }$. After moving through oil-1 and another medium; oil-2, it enters glass and then it enters water. If the refractive indices of glass and water are 1.5 and 1.3, respectively, find the angle which the ray makes with normal in water.

1. $si{n}^{-1}\left(\frac{1}{2.4}\right)$
2. $si{n}^{-1}\left(\frac{1}{2.5}\right)$
3. $si{n}^{-1}\left(\frac{1}{2.6}\right)$
4. $si{n}^{-1}\left(\frac{1}{2.8}\right)$

Q.

A postage stamp kept below a rectangular glass block of refractive index 1.5 when viewed from vertically above, it appears to be raised by 7.0 mm. Calculate the thickness of the glass slab.

1. 20 cm

2. 2.1 cm

3. 11 cm

4. 3 cm

Q.

A postage stamp kept below a rectangular glass slab of refractive index 1.5 when viewed from vertically above it, appears to be raised by 7.0 mm. Calculate the thickness of the glass slab.

Q.

A microscope is focused on an ink mark on the top of a table. If we place a glass slab $3cm$ thick on it, how should the microscope be moved to focus on the ink spot again? The refractive index of the glass slab is $1.5$.

Q.

A coin is placed in a tumbler, water is then filled in the tumbler to a height of 20 cm. If the refractive index of water is 4/3, calculate the apparent depth of the coin. [2 MARKS]

Q.

Give an example of a physical quantity which is dimensionless.

Q.

A fish is swimming in a river at a depth of $20cm$ from the surface of the water. The refractive index of water is $4/3$. An eagle flying above the water will see the fish at a depth of ___$cm$

Q. Which of the following are responsible for the formation of a mirage?

1. Refraction
2. Temperature
3. Density
4. Critical angle
5. Dispersion
6. Scattering
7. Absorption
8. Refractive index

Q.

A ray of light of wavelength 4800 Angstrom suffers refraction from air to glass. Taking ${}_a{\mu }_g$​ = $\frac{3}{2}$, find the wavelength of light in glass.

1. 6400

2. 3600

3. 1600

4. 3200

Q.

For a critical angle of ${60}^{\circ }$ and the refractive index of the first medium is 1.732, the refractive index of the second medium is:

1. 1

2. 1.5
3. 2
4. 2.5

Q.

A coin is placed at the bottom of a beaker containing water $\left(\mathrm{refractive}\mathrm{index}=\frac{4}{3}\right)$ to a depth of $12\mathrm{cm}$. By what height the coin appears to be raised when seen from vertically above?

1. $3\mathrm{cm}$

2. $6\mathrm{cm}$

3. $9\mathrm{cm}$

4. $16\mathrm{cm}$

Q.

Water in a pond appears to be only three-quarter of its actual depth. (a) What property of light is responsible for this observation? Illustrate your answer with the help of a ray diagram. (b) How the refractive index of water calculated from its real and apparent depths?

Q.

A water pond appears to be 2.7 m deep. If the refractive index of water is $\frac{4}{3}$, find the actual depth of the pond.

Q.

Why does the depth of water in a pond appear only three-fourths of its original depth? Explain with the help of a diagram.

Q. Lights of all color travel at the same speed through any transparent medium.

1. True
2. False

Q. The refractive indices of glass and water are 3/ 2 and 4/ 3 respectively. The refractive index of glass with respect to water is

1. 9/8
2. 5/3
3. 2
4. 8/9

Q.

The Refractive index of a medium is

1. directly proportional to the wavelength of light in air

2. inversely proportional to the wavelength of light in air

3. inversely proportional to the square of the wavelength of light in air

4. directly proportional to the square of the wavelength of light in air

Q.

The speed of light in a medium with refractive index $\mathrm{\mu }$ is given by v=

Q. Assertion :If the angles of the base of the prism are equal, then in the position of minimum deviation, the refracted ray will pass parallel to the base of prism. Reason: In the case of minimum deviation, the angle of incidence is equal to the angle of emergence.

1. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
2. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
3. Assertion is correct but Reason is incorrect
4. Both Assertion and Reason are incorrect

Q. A postage stamp kept below a rectangular glass slab of refractive index 1.5 when viewed from vertically above it, appears to be raised by 7.0 mm. Calculate the thickness of the glass slab.[3 marks]

Q.

A coin is placed at the bottom of a beaker containing water (refractive index = $\frac{4}{3}$) to a depth of 12 cm. By what height the coin appears to be raised when seen from vertically above?

Q. The refractive index of denser medium with respect to rarer medium is 1.125. The difference between the velocities of light in the two media is $0.25\times {10}^8$ m/s. The velocities of light in the two media are (c $=3\times {10}^8$ m/s):

1. $2.0\times {10}^8$ m/s; $2.25\times {10}^8$ m/s
2. $2\times {10}^8$ m/s; $2.5\times {10}^8$ m/s
3. $2.5\times {10}^8$ m/s; $3\times {10}^8$ m/s
4. $2\times {10}^8$ m/s; $3\times {10}^8$ m/s

Q.

Vikas is observing his photograph by keeping a rectangular glass slab of thickness $15\mathrm{cm}$on it. He wondered as he observed that his photograph was closer to him. By what distance his photograph is raised from the bottom of the glass slab?$(\mathrm{Take}{\mu }_{\mathrm{g}}=1.5)$

1. $7.5\mathrm{cm}$

2. $6\mathrm{cm}$

3. $5\mathrm{cm}$

4. $10\mathrm{cm}$

Q.

What do you understand by the term refractive index of Glass is 1.5?