Refractive Index

Q. e vernier scale of a travelling microscope has25 divisions which coincide with 24 main scaledivisions. If each main scale division is 0.5 mmthen least count of this microscope is2 0, 02 mm(4) 0.01 mm(3) 0.1 mnm

Q. A ray of light is incident at the glass–water interface at an angle i, it emerges finally parallel to the surface of water, then the value of ${\mu }_g$ would be

1. $\left(\frac{4}{3}\right)sini$
2. $\frac{1}{sini}$
3. $\frac{4}{3}$
4. $1$

Q. A double convex lens, lens made of a material of refractive index ${\mu }_1$ is placed inside two liquids or refractive indices ${\mu }_2$ and ${\mu }_3$, as shown ${\mu }_2>{\mu }_1>{\mu }_3$. A wide, parallel beam of light is incident on the lens from the left.

1. A single convergent beam
2. Two different convergent beams
3. Two different divergent beams
4. A convergent and a divergent beam

Q. A pole of length 1.00 m stands half dipped in a swimming pool with water level 50.0 cm higher than the bed. The refractive index of water is 1.33 and sunlight is coming at an angle of 45° with the vertical. Find the length of the shadow of the pole on the bed.

Q. A small piece of wood is floating on the surface of a 2.5 m deep lake. Where does the shadow form on the bottom when the sum is just setting? Refractive index of water = 4/3.

Q. In the following ray diagrams, a ray of light is incident at an equal angle of incidence at the interface of four different materials. Which material is optically densest?

1. 
2. 
3. 
4. 

Q. The speed of yellow light in a certain liquid is 2⋅4 × 10⁸ m s⁻¹. Find the refractive index of the liquid.

Q. The value of absolute refractive index is always greater than 1.

1. False
2. True

Q. A ball is dropped from a height of $20\text{m}$ above the surface of water in a lake. The refractive index of water is $\frac{4}{3}$. A fish inside the lake, in the line of fall of the ball, is looking at the ball. At an instant, when the ball is $12.8\text{m}$ above the water surface, the fish sees the speed of ball as

1. $21.33{\text{ms}}^{-1}$
2. $16{\text{ms}}^{-1}$
3. $12{\text{ms}}^{-1}$
4. $9{\text{ms}}^{-1}$

Q. Solve the previous problem if the paperweight is inverted at its place so that the spherical surface touches the paper.

Q. A cylindrical vessel of diameter 12 cm contains 800π cm³ of water. A cylindrical glass piece of diameter 8.0 cm and height 8.0 cm is placed in the vessel. If the bottom of the vessel under the glass piece is seen by the paraxial rays (see figure), locate its image. The index of refraction of glass is 1.50 and that of water is 1.33.
Figure

Q. One end of a cylindrical glass rod (μ = 1.5) of radius 1.0 cm is rounded in the shape of a hemisphere. The rod is immersed in water (μ = 4/3) and an object is placed in the water along the axis of the rod at a distance of 8.0 cm from the rounded edge. Locate the image of the object.

Q. Will the diffraction effects from a slit be more or less clearly visible if the slit-width is increased?

Q. The index of refraction of fused quartz is 1⋅472 for light of wavelength 400 nm and is 1⋅452 for light of wavelength 760 nm. Find the speeds of light of these wavelengths in fused quartz.

Q.

White light is incident normally on a glass plate (in air) of thickness 500 nm and refractive index of 1.5. The wavelength (in nm) in the visible region (400 nm - 700 nm) that is strongly reflected by the plate is:

1. 450

2. 600

3. 400

4. 500

Q. Refractive index of the medium on the left and right side of the spherical surface are $1$ and $1.5$ respectively. For the arrangement of object and spherical refracting surface as shown in figure, the position of image will be

1. $+20\text{cm}$
2. $+45\text{cm}$
3. $-45\text{cm}$
4. $+30\text{cm}$

Q. A biconvex lens has a radius of curvature of magnitude $20\text{cm}$ and the refractive index of the lens is $1.5$. Which of the following option describe best the image formed of an object of height $2\text{cm}$ placed $30\text{cm}$ from the lens?

Q. An air bubble is formed inside water. Does it act as a converging lens or a diverging lens?

Q. A container contains water up to a height of 20 cm and there is a point source at the centre of the bottom of the container. A rubber ring of radius r floats centrally on the water. The ceiling of the room is 2.0 m above the water surface. (a) Find the radius of the shadow of the ring formed on the ceiling if r = 15 cm. (b) Find the maximum value of r for which the shadow of the ring is formed on the ceiling. Refractive index of water = 4/3.

Q. A light ray falling at an angle of 45° with the surface of a clean slab of ice of thickness 1.00 m is refracted into it at an angle of 30°. Calculate the time taken by the light rays to cross the slab. Speed of light in vacuum = 3 × 10⁸ m s⁻¹.

Q. when a light ray passes from air to denser medium its speed is reduced by 30+. What is thr refractive index of the medium.

Q. A point source is placed at a depth h below the surface of water (refractive index = μ). (a) Show that light escapes through a circular area on the water surface with its centre directly above the point source. (b) Find the angle subtended by a radius of the area on the source.

Q. Suppose the medium in the previous question is water. Select the correct option(s) from the list given in that question.