Refraction at a Spherical Surface

Q. In the figure shown, a point object $O$ is placed in air. A spherical boundary of radius of curvature $1.0m$ separates two media. $AB$ is the principal axis. The refractive index above $AB$ is $1.6$ and below $AB$ is $\mathrm{2.0.}$ The separation between the images formed due to refraction at the spherical surface is

1. $12m$
2. $20m$
3. $14m$
4. $10m$

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

Q. A parallel narrow beam of light is incident on the surface of a transparent hemisphere of radius $R$ and refractive index $\mu =1.5$ as shown. The position of the image formed by refraction at the spherical surface only is

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

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 $90\text{cm}$

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

Q. Refraction takes place at a convex spherical boundary separating air-glass medium. For the image to be real, the object distance $({\mu }_g=\frac{3}{2})$

1. Should be greater than two times the radius of curvature of the refracting surface
2. Should be greater than six times the radius of curvature of the refracting surface
3. Should be greater than the radius of curvature of the refracting surface
4. Is independent of the radius of curvature of the refracting surface

Q. A ray of light falls on the surface of a spherical glass paperweight making an angle $\alpha$ with the normal and is refracted in the medium at an angle $\beta$. The angle of deviation of the emergent ray from the direction of the incident ray

1. $(\alpha -\beta )$
2. $2(\alpha -\beta )$
3. $(\alpha -\beta )/2$
4. $(\beta -\alpha )$

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

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. 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. $R^2$