Curved Surface Formula

Q. One end of a cylindrical glass rod ends in a hemispherical surface of radius R = 20 mm. Find the image distance of a point object on the axis of the rod, 80 mm to the left of the vertex. The rod is in the air.

1. 120 mm
2. -120 mm
3. -80 mm
4. 60 mm

Q. The apparent depth of an object lying in a denser medium is always ______ the real depth

1. greater than
2. lesser than
3. equal to
4. opposite to

Q.

An object is placed 5 cm from an convex air-glass interface of radius of curvature 10 cm as shown. If the refractive index of glass is 1.5, determine the location of image from the interface.

1. 10 cm, left
2. 10 cm, right
3. 5 cm, left
4. 5 cm, right

Q. A person standing on the land beside a river looks at a fish inside the water. The depth of the fish inside the water will appear ______________ to the person.
(Note that you are almost vertically above the fish)

1. exactly double of its actual depth
2. farther than its actual depth
3. same as its actual depth
4. closer than its actual depth

Q. For refraction at a curved surface; the u.v relationship is:
$\frac{{\mu }_2}{v}-\frac{{\mu }_1}{u}=\frac{{\mu }_2-{\mu }_1}{R}$

1. ${\mu }_2$: Refractive index of the medium of refracted ray
2. ${\mu }_1$: Refractive index of the medium of incident ray
3. R: Radius of curvature of the refractive surface.
4. R is always positive

Q. One end of a cylindrical glass rod ends in a hemispherical surface of radius R = 20 mm. The rod is immersed in water of index 1.33. Find the image distance if object distance is 80 mm.

1. 185

Q. One end of a cylindrical glass rod ends in a hemispherical convex surface of radius $R=20mm$. Find the image distance of a point object on the axis of the rod, placed $80mm$ outside its vertex. The rod is in the air and the refractive index of glass is $1.5$.

1. $120mm$
2. $120mm$
3. $-80mm$
4. $60mm$

Q. When is the curved surface formula applicable?

1. Curved surface is spherical in shape.
2. Surface is planar in shape.
3. Aperture of surface is huge.
4. Refracting surface is convex in shape.

Q.

A fish inside a river will appear at a/an _________ depth to an observer looking from the ground.

1. lesser

2. greater

3. exact

4. inadequate data

Q. One end of a cylindrical glass rod ends in a hemispherical convex surface of radius $R=20mm$. Find the image distance of a point object on the axis of the rod, placed $80mm$ outside its vertex. The rod is in the air and the refractive index of glass is $1.5$.

1. $120mm$
2. $120mm$
3. $-80mm$
4. $60mm$

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 three times the radius of curvature of the refracting surface
2. should be greater than two 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 light ray is traveling from medium A to B. If the value of $\frac{\sin i}{\sin r}$ is1 implies that the light ray bends towards the normal.

1. greater than
2. lesser than
3. equal to

Q. A point object is placed at the center of a glass sphere of radius 6 cm and refractive index 1.5. find the distance of the virtual image from the surface of the sphere.

Q. One end of a cylindrical glass rod ends in a hemispherical surface of radius $R=20mm$. Find the image distance (in mm) of a point object on the axis of the rod, $80mm$ to the left of the vertex. The rod is in air.

1. 120

Q. Block hole is an object whose gravitational field is so strong that even light cannot escape from it. To what approximate radius would earth $(mass=5.98\times {10}^{24}kg)$ have to be compressed to be a black hole?

1. ${10}^{-9}m$
2. ${10}^{-2}m$
3. $100m$
4. ${10}^{-6}m$