## Question

A convex lens of focal length 20 cm is cut into two equal parts so as to obtain two plano-convex lenses as shown in figure. The two parts are then put in contact as shown in figure. What is the focal length of the combination?

### Solution

20 cm

A single double convex lens may be regarded as a combination of two plano-convex lenses. Let *f *be the focal length of each plano-convex part. Then

In the problem, again two plano-convex lenses each of focal length 40 cm are put in contact. Now, the combined focal length is given by

#### SIMILAR QUESTIONS

A real image is formed by a convex lens. If we put it in contact with a concave lens and the combination again forms a real image, which of the following is true for the new image from the combination?

Focal length of a convex lens will be maximum for:

A concave mirror is focal length *f* in air is used in a medium of refractive index 2. What will be the focal length of the mirror in the medium?

A luminous object is placed at a distance of 30 cm from a convex lens of focal length 20 cm. On the other side of the lens, at what distance from the lens must a convex mirror of radius of curvature 10 cm be placed in order to have an upright image of the object coincident with it

The far-point of a short-sighted eye is 200 cm. The power of the lens is:

The near point of a short-sighted person is 10 cm and he desires to read a book 30 cm away from him. The power of the lens to be used by him is:

The distance between an object and the screen is 100 cm. A lens produces an image on the screen when placed at either of the positions 40 cm apart. The power of the lens is:

A thin equiconvex lens has focal length 10 cm and refractive index 1.5. One of its faces is now silvered and for an object placed at a distance *u* in front of the lens, the image coincides with the object. The value of *u* is:

The plane face of a plano-convex lens of focal length 20 cm is silvered. What type of mirror will it become and of what focal length *f *?

As shown in figure, a convergent lens is placed inside a cell filled with liquid. The lens has focal length +20cm when in air, and its material has refractive index 1.50. If the liquid has refractive index 1.60, the focal length of the system is: