Question:
A planoconvex lens is made of glass of refractive index 1.5. The radius of curvature of its spherical
surface is 40 cm. At what distance from the lens will a parallel beam of light will get focussed?
Draw a neat, clear labelled ray diagram to show image formation from the lens. What will be the
nature and power of a combination of two such lenses kept with their (i) plane surfaces in contact
(ii) spherical surfaces in contact.
Answer:
For a lens in air, the power 1/f is then given by
1/f = (n − 1) [1/R1 − 1/R2]
The radii of curvature,
R1 = 40 cm, R2 = ∞
Thus, f = R1/n − 1 = 40/1.5 − 1 = 80 cm
A parallel beam of light will be focused at 80 cm from the lens.
(i)
For a double convex lens, the radius R1 is positive and radius R2 is negative
1/f = (n − 1) [1/R1 − 1/R2]
or, 1/f = (1.5 − 1) [ 1 0.40 + 1 0.40] = 2.5 D
1/f > 0 and this lens is converging.
(ii)
When spherical surfaces in contact the combined focal length f of the lenses is given by
1/f = 1/f1 + 1/f2 = 1/0.8 + 1/0.8 = 2.5 D
1/f > 0 and this lens will be converging.
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