Question

A laser beam of diameter *d*_{1} = 1.4 mm is
directed along the optical axis of a thin lens of focal length +5.1
cm (see figure below).

(a) How far from the lens will the beam be focused?

(b) A second positive lens is placed to the right of the first.
Light emerges from the second lens in a parallel beam of diameter
*d*_{2} = 3.5 mm. Thus the combination of lenses
acts as a beam expander. Find the focal length of the second
lens.

Find the distance between the lenses.

Answer #1

The diagram for the above situation can be shown as ::--

the focal length of first lens = f1 and of second = f2

**PART A)**

the beam coming from infinity will focus at the focal length of the first lens.

i.e. at the distance of **d =** f1 = **5.1 cm
from the lens.**

**PART B)**

For the rays to emerge parallel from the other lens, the converging point of the rays must be at a distance equal to that of focal length of second lens.

From geometry as shown we can write:-

tan() = (d1/2)/f1

tan() = (d2/2)/f2

so we can write

(d1/2)/f1 = (d2/2)/f2

f2 = d2 (f1/ d1) = 3.5 mm (+5.1 cm )/1.4 mm

=> **f2 = + 12.75 cm**

**==**

**hope it helps!**

**do give feedback!**

**have a nice day!**

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