# An Object 1.5 Cm in Size is Placed on the Side of the Convex Lens in the Arrangement (A) Above. the Distance Between the Object and the Convex Lens is 40 Cm. Determine the Magnification Produced by the Two-lens System, and the Size of the Image - Physics

An object 1.5 cm in size is placed on the side of the convex lens in the arrangement (a) above. The distance between the object and the convex lens is 40 cm. Determine the magnification produced by the two-lens system, and the size of the image

#### Solution

Height of the image, h1 = 1.5 cm

Object distance from the side of the convex lens, u_1 = -40 cm

|u_1| = 40 cm

According to the lens formula:

1/v_1 - 1/u_1 = 1/f_1

Where

v_1 = Image distance

1/v_1 = 1/30 + 1/(-40) = (4-3)/120 = 1/120

:. v_1 = 120 cm

Magnification,  m = v_1/|u_1|

= 120/40 = 3

Hence, the magnification due to the convex lens is 3.

The image formed by the convex lens acts as an object for the concave lens.

According to the lens formula:

1/v_2 - 1/u_2 = 1/f_2

Where

u_2 = Object distance

= +(120 - 8) =112 cm

v_2 = Image distance

1/v_2  = 1/-20 + 1/112  = (-112 + 20)/2240 = (-92)/2240

:.v_2 = -2240/92 cm

Magnification, m' = |v_2/u_2|

= 2240/92 xx 1/112 = 20/92

Hence, the magnification due to the concave lens is 20/92.

The magnification produced by the combination of the two lenses is calculated as: m xx m'

= 3 xx 20/92 = 60/92 = 0.652

The magnification of the combination is given as:

h_2/h_1 = 0.652

h_2 = 0.652 xx h_1

Where

h1 = Object size = 1.5 cm

h2 = Size of the image

:. h_2 = 0.652 xx 1.5 = 0.98 cm`

Hence, the height of the image is 0.98 cm.

Concept: Refraction at Spherical Surfaces and by Lenses - Refraction by a Lens
Is there an error in this question or solution?

#### APPEARS IN

NCERT Class 12 Physics Textbook
Chapter 9 Ray Optics and Optical Instruments
Q 21.2 | Page 347