## Question

####

Two lenses of powers +12 D and –2D are placed in contact. This combination is placed between an object and a screen which are 60 cm apart. If this combination is kept in two positions between object and screen, a real image of the object is formed on the screen. Calculate the distance between the two positions of the combination.

### Solution

Correct option is
34.6 cm

The power *P* of the combination is

∴ focal length of the combination is

If *a* be the distance between object and screen, and *d* the distance between the two positions of the combination, then

Here *a* = 60 cm.

.

#### SIMILAR QUESTIONS

Q1

The focal length of a lens of glass (*n* = 1.5) in air is 0.4 m and in a liquid is 1.2m. Determine the refractive index of the liquid.

Q2

The radius of curvature of both the surfaces of a double convex lens is *R*. The refractive index of the material of the lens is 1.5. When a point-source of light is placed on the principal axis of the lens at a distance of 20 cm in-front of the one surface of the lens, then rays emerge from the other surface normally. Determine the radius of curvature *R* of each surface of the lens.

Q3

An air passenger sitting in an aeroplane flying at a height of 2000 meter from the earth takes photographs of the earth. The focal-length of his camera-lens is 50 cm. The size of the camera-film is (18 × 18)cm^{2}. What maximum area can be covered by the camera?

Q4

The diameter of sun is 1.4 × 10^{9} meter. Determine the diameter of the image of the sun formed by a convex-lens of focal length 1.0 meter. Distance of the sun from the earth is 1.0 × 10^{11} meter.

Q5

A small object is placed at a distance of 15 cm from two coaxial thin lenses in contact. The focal length of each lens is 25 cm. What will be the distance between the object and its image when both the lenses are (i) convex, (ii) concave.

Q6

The image of an object is formed at a distance of 40 cm from the object, when the lens is placed exactly mid-way between the object and the image. What is the power of the lens?

Q7

A real image is formed by a lens at a distance of 20 cm from the lens. The image shifts towards the combination by 10 cm when a second lens is brought in contact with the first lens. Determine the power of the second lens.

Q8

Two lenses of powers +2.50 D and –3.75 D are combined to form a lens combination. Determine the focal-length of this combination.

Q9

The refractive indices of the material of a lens for yellow and red colours are 1.54 and 1.51 respectively. The focal length of the lens for yellow light is 34.0 cm. Calculate the focal length of the lens for red light.

Q10

The refractive indices of the material of a lens for violet and red colours are 1.56 and 1.54 respectively. If the focal length of the lens for violet light is 40 cm, then calculate (i) focal length of the lens for red light. (ii) Longitudinal chromatic aberration of the lens and (iii) Dispersive power of the material of the lens.