Ncert Exercises & Solutions

9.8 A beam of light converges at a point P. Now a lens is placed in the path of the convergent beam 12cm from P. At what point does the beam converge if the lens is (a) a convex lens of focal length 20cm, and (b) a concave lens of focal length 16cm?

(a)
Hint: Use the lens formula.

Step: Find the position of the final image.
The object is virtual and the image formed is real.
Object distance, u = +12 cm
The focal length of the convex lens, f = +20 cm

$Using the lens formula :$
$\frac{1}{f} = \frac{1}{v} - \frac{1}{u}$
$\frac{1}{v} = \frac{1}{20} + \frac{1}{12} = \frac{3 + 5}{60}$
$v = \frac{60}{8} = 7.5 cm$
So the final image is formed at a distance of 7.5 cm away from the lens on the right side.

(b)
Hint: Use the lens formula.

Step: Find the position of the final image.
The focal length of the concave lens, f = -16 cm

$Using the lens formula :$
$\frac{1}{f} = \frac{1}{v} - \frac{1}{u}$
$\frac{1}{v} = - \frac{1}{16} + \frac{1}{12} = \frac{- 3 + 4}{48}$
$v = \frac{48}{1} = 48 cm$
So the final image is formed at a distance of 48 cm away from the lens on the right side.

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