Refraction at a Spherical Surface

Q. A ray of light falls on a transparent sphere with centre at C as shown in figure. The ray emerges from the sphere parallel to line AB. The refractive index of the sphere is:

1. $\sqrt{3}$
2. $\sqrt{2}$
3. $\frac{3}{2}$
4. $\frac{1}{2}$

Q. A concave spherical surface of radius of curvature $10$ cm separates two mediums $x$ and $y$ of refractive index $\frac{4}{3}$ and $\frac{3}{2}$ respectively. If the object is placed along principal axis in medium $X$ then

1. Image is virtual if the object distance is less than $90$ cm
2. Image is real if the object distance is greater than $90$ cm
3. Image is always real
4. Image is always virtual

Q. A transparent cylinder has its right half polished so as to act as a mirror. A paraxial light ray is incident from left, that is parallel to principal axis, exits parallel to the incident ray as shown. The refractive index of the material of the cylinder is:

1. 1.2
2. 1.5
3. 1.8
4. 2

Q. Find the apparent depth of the object, as seen by the observer.
[measured from the surface $\text{AB}$]

1. $36\text{cm}$
2. $18\text{cm}$
3. $24\text{cm}$
4. $16\text{cm}$

Q.

Light falls from glass $(\mu =1.50)$ to air. Find the angle of incidence for which the angle of deviation is ${90}^{\circ }$.

Q. A plano concave lens is placed on a paper on which a flower is drawn. How far above its actual position does the flower appear to be ?

1. $10\text{cm}$
2. $15\text{cm}$
3. $50\text{cm}$
4. None

Q. A biconvex lens of focal length 15 cm is in front of a plane mirror. The distance between the lens and the mirror is 10 cm. A small object is kept at a distance of 30 cm from the lens. The final image is

1. Virtual and at a distance of 16 cm from the mirror
2. Virtual and at a distance of 20 cm from the mirror
3. Real and at a distance of 16 cm from the mirror
4. Real and at a distance of 20 cm from the mirror

Q. A transparent thin film of uniform thickness and refractive index $n_1=1.4$ is coated on the convex spherical surface of radius R at one of a long solid glass cylinder of refractive index $n_2=1.5,$ as shown in the figure. Rays of light parallel to the axis of the cylinder traversing through the film from air to glass get focused at a distance $f_1$ from the film, while rays of light traversing from glass to air get focused at a distance $f_2$ from the film. Then

1. $|f_1|=3R$
2. $|f_1|=2.8R$
3. $|f_2|=2R$
4. $|f_2|=1.4R$

Q.

A light ray suffers minimum deviation while passing through a prism of refractive index $1.5$and refracting angle $60°$. Calculate the angle of deviation and angle of incidence.

Q. There is an equiconvex glass lens with radius of each face as R and ${}_a{\mu }_g=\frac{3}{2}an{d}_a{\mu }_w=\frac{4}{3}$. If there is water in object space and air in image space, then the focal length is

1. 2R
2. R
3. $3\frac{R}{2}$
4. $R^2$

Q. As shown in the figure, region $BCDEF$ and $ABFG$ are of refractive index $2.0$ and $1.5$ respectively. A particle $O$ is kept at the mid-point of $DH$. Image of the object as seen by the eye is at a distance of :

1. $10\text{cm}$ from point $D$
2. $22.5\text{cm}$ from point $D$
3. $30\text{cm}$ from point $D$
4. $20\text{cm}$ from point $D$

Q. (a) Using the phenomenon of polarization, show how transverse nature of light can be demonstrated.

(b) Two polaroids $P_1$ and $P_2$ are placed with their pass axes perpendicular to each other. Unpolarised light of intensity $I_0$ is incident on $P_1$. A third polaroid $P_3$ is kept in between $P_1$and $P_2$ such that its pass axis makes an angle of ${30}^{\circ }$ with that of $P_1$. Determine the intensity of light transmitted through $P_1,P_2$ and $P_3$.

Q. An air bubble in a glass sphere having 4 cm diameter appears 1 cm from surface nearest to eye when looked along diameter. If ${\mu }_{g,a}=1.5$, the distance of bubble from refracting surface is

1. 3.2 cm
2. 2.8 cm
3. 1.2 cm
4. 1.6 cm

Q. In the given figure a plano - concave lens is placed on a paper on which a flower is drawn. How far above its actual position does the flower appear to be ?

1. $10\text{cm}$
2. $15\text{cm}$
3. $50\text{cm}$
4. None of these

Q. A glass prism is immersed in a hypothetical liquid. The curves showing the refractive index $n$ as a function of wavelength $\lambda$ for glass and liquid are as shown in the figure. When the ray of white light is incident on the prism parallel to the base:

1. yellow ray travels without deviation
2. blue ray is deviated towards the vertex
3. red ray is deviated towards the base
4. there is no dispersion

Q. A narrow beam of light of diameter D falls on a hemispherical glass sphere of radius R (R >>> D) and refractive index $\frac{3}{2}$. Diameter of beam on the base of hemisphere is.

1. $\frac{D}{2}$
2. $\frac{D}{3}$
3. $\frac{2D}{3}$
4. $\frac{3}{4}D$

Q. A point luminous object is placed at a distance of $30\text{cm}$ from the convex lens of focal length $20\text{cm}$ on the other side of the lens. At what distance from the lens, a convex mirror of radius of curvature $10\text{cm}$ be placed in order to have an upright image of the object coincident with it?

1. $12\text{cm}$
2. $30\text{cm}$
3. $50\text{cm}$
4. $60\text{cm}$

Q.

Light is incident from glass $(\mu =1.5)$ to air. Sketch the variation of the angle of deviation $\delta$ with the angle of incident i for $0<i<{90}^{\circ }$.

Q.

A ray of light is incident on the surface of a sphere of refractive index $\mu =\sqrt{\frac{5}{2}}$ . After refraction, it is total internally reflected and refracted out of the sphere again such that the total deviation is minimum. The angle of incidence of the ray is

1. ${53}^0$
2. ${30}^0$
3. ${60}^0$
4. ${45}^0$

Q.

One end of a cylindrical glass rod shown in figure ends in a hemispherical surface of radius R = 20 mm.
-Let the same rod be immersed in water of index 1.33, the other quantities having the same values as before. Find the image distance.

1. 120 mm

2. -120 mm

3. 180 mm

4. -180 mm

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.

A plane glass slab is kept over various coloured letters. The letter which appears least raised is

1. Violet

2. Blue

3. Green

4. Red

Q. A small air bubble is present exactly at the centre of a glass sphere. size of image as seen from outside is of

Q.

Locate the image of the point object O in the situation shown in the figure with respect to the pole $P$ of the spherical surface. The point C denotes the centre of curvature of the refracting surface.

1. $30cm$, Left

2. $30cm$, Right

3. $20cm$, Right

4. $20cm$, Left
   

Q. A ray of light strikes a glass slab of thickness t. It emerges on the opposite face, parallel to the incident ray but laterally displaced. The lateral displacement is

1. 0
2. $t\sin (i-r)\cos r$
3. $t\frac{\sin i}{\cos r}$
4. $t\frac{\sin (i-r)}{\cos r}$

Q.

A ray of light undergoes refraction and loses $0.25$ times its velocity. If i is the angle of incidence and is very small, the angle of deviation for the ray of light is______

Q. The image for the converging beam after refraction through the curved surface is formed at :

1. $x=\frac{180}{7}\text{cm}$
2. $x=40\text{cm}$
3. $x=\frac{40}{3}\text{cm}$
4. $x=-\frac{40}{3}\text{cm}$

Q. An object lying at the distance of $5\text{cm}$ from a spherical interface as shown in the figure, is moving with the velocity of $5\text{cm/s}$. If the interface is moving with a velocity of $3\text{cm/s}$, then calculate the velocity of the image formed by the spherical surface.
(Assume that spherical interface always seperates air and medium of refractive index $1.5$)

Q.

An air bubble in sphere having 4 cm diameter appears 1 cm from surface nearest to eye when looked along diameter. If _am_g = 1.5, the distance of bubble from refracting surface is

[CPMT 2002]

1. 1.2 cm

2. 3.2 cm

3. 2.8 cm

4. 1.6 cm

Q. A concave spherical surface of radius of curvature $10\text{cm}$ separates two medium $X$ & $Y$ of refractive index $\frac{4}{3}$ & $\frac{3}{2}$ respectively. If the object is placed along principal axis in medium $X$ then

1. image is always real
2. image is real if the object distance is greater than $90\text{cm}$
3. image is always virtual
4. image is virtual if the object distance is less than $90\text{cm}$