Question

A laser beam of diameter d₁ = 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 d₂ = 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

==

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