## Question

How far should an object be held from a concave mirror of focal length 40 cm so as to obtain an image twice the size of the object?

### Solution

20 cm or 60 cm

*f* = – 40 cm

There are two possibilities: (a) the image is real and (b) the image is virtual.

(a) If the image is real then

Putting *v* = 2*u* in the mirror formula gives *u* = – 60 cm

(b) If the image is virtual, then

Putting *v* = –2*u* in the mirror formula gives *u* = –20 cm.

Hence the possible object distance is **20 cm or 60 cm** depending on whether the image is virtual or real.

#### SIMILAR QUESTIONS

A convex lens forms a real image of an object on a screen; the magnification of the image being 3/2. The object and the screen are kept fixed and the lens is moved through a distance of 16 cm when a sharp image is again formed on the screen; the magnification now being 2/3. What is the focal length of the lens?

An object is placed at a distance of 10 cm from a co-axial combination of two lenses *A* and *B*. The combination forms a real image three times the size of the object. If lens *B* is concave with a focal length of 30 cm, what is the nature and focal length of lens *A*?

A plano-convex lens acts like a concave mirror of 28 cm focal length when its plane surface is silvered and like a concave mirror of 10 cm focal length when its curved surface is silvered. What is the refractive index of the material of the lens?

A pin is placed 10 cm in front of a convex lens of focal length 20 cm and refractive index 1.5. The surface of the lens farther away from the pin is silvered and has a radius of curvature of 22 cm. How far from the lens is the final image formed?

The radius of curvature of the convex face of a plano-convex lens is 12 cm and its refractive index is 1.5. What is the focal length of the lens?

A point object is placed at a distance of 12 cm on the axis of a convex lens of focal length 10 cm. On the other side of the lens, a convex mirror is placed at a distance of 10 cm from the lens such that the image formed by the combination coincides with the object itself. What is the focal length of the convex mirror?

Two glasses have dispersive powers in the ratio of 2 : 3. These glasses are used in the manufacture of an achromatic objective of focal length 20 cm. What are the focal lengths of the two lenses of the objective?

An object 5 cm tall is placed 10 cm from a convex mirror. What is the nature and the size of the image?

A convex mirror of radius of curvature 20 cm forms an image which is half the size of the object. How far is the object from the mirror?

A concave mirror produces a real image twice the size of the object when place at a distance of 22.5 cm from it. At what distance from the mirror should the object be placed so that the image becomes three times the size of the object?