(a) Under what condition will a glass lens placed in a transparent liquid become invisible?
(b) Describe and illustrate with a diagram, how we should arrange two converging lenses so that a parallel beam of light entering one lens emerges as a parallel beam after passing through the second lens.
(c) An object is placed at a distance of 3 cm from a concave lens of focal length 12 cm. Find the (i) position and (ii) nature of the image formed.
(a) When the refractive index of glass lens becomes equal to the refractive index of transparent liquid, the glass lens will become invisible.
(b) Parallel beam converges at focus of the first lens and emerges parallel as it is at the focus of second lens.
(c) f = -12 cm, u = -3 cm
(i) Using 1/f = 1/v - 1/u, we get
1/v = 1/f + 1/u = 1/-12 - 1/3 = -1-4/12
v = - 12/5 cm
(ii) v < 0, so image is virtual.
|v| <|u|, so image id diminished.
m = v/u = (-12/5)/-3 = 4/5
m > 0 but |m| < 1, so, image is erect and diminished.