Question

A converging lens (f₁ = 11.9 cm) is located 27.6 cm to the left of a diverging lens (f₂ = -5.94 cm). A postage stamp is placed 34.8 cm to the left of the converging lens. Find the overall magnification.

Answer 1

first find image distance for converging lens

f = 11.9 cm

u = 34.8 cm

1/f = 1/u + 1/v

v = f*u/(u - f) = 11.9*34.8/(34.8 - 11.9) = 18.08 cm

Now this image will work like object for diverging lens, So now

f1 = -5.94 cm

u1 = 27.6 - 18.08 = 9.52 cm

1/f1 = 1/u1 + 1/v1

v1 = f1*u1/(u1 - f1)

v1 = 9.52*(-5.94)/(9.52 - (-5.94))

v1 = -3.66 cm

Now overall magnification will be

Mnet = M*M1

Mnet = (-v/u)*(-v1/u1)

Mnet = (-18.08/34.8)*(-(-3.66)/9.52)

Mnet = -0.1997

Mnet = -0.20