The size of the image of an object, which is at infinity, as formed by a convex lens of focal length 30 cm is 2 cm. If a concave lens of focal length 20 cm is placed between the convex lens and the image at a distance of 26 cm from the convex lens, calcul

Question

The size of the image of an object, which is at infinity, as formed by a convex lens of focal length 30 cm is 2 cm. If a concave lens of focal length 20 cm is placed between the convex lens and the image at a distance of 26 cm from the convex lens, calculate the new size of the image. [2003]

Smart Achievers · Accepted Answer

(2)

The image formed by the convex lens, $I_{1}$ acts as a virtual object for the concave lens. The concave lens forms the image of $I_{1}$ at $I_{2}$ .

Size of the image at $I_{1} = 2 cm$

For the concave lens, $\frac{1}{v} - \frac{1}{u} = \frac{1}{f}$

or, $\frac{1}{v} - \frac{1}{4} = - \frac{1}{20}$ or, $\frac{1}{v} = - \frac{1}{20} + \frac{1}{4} = \frac{4}{20} = \frac{1}{5}$

or, $v = 5 cm$

Distance of $I_{2}$ from the concave lens.

$∴$ $Magnification, m = \frac{v}{u} = \frac{size of image}{size of object} = \frac{5}{4}$

or, $\frac{size of image}{2} = 1.25$

$∴$ $Size of image due to concave lens = 2.5 cm$

Solution

Q.
The size of the image of an object, which is at infinity, as formed by a convex lens of focal length 30 cm is 2 cm. If a concave lens of focal length 20 cm is placed between the convex lens and the image at a distance of 26 cm from the convex lens, calculate the new size of the image. [2003]

1 1.25 cm

2 2.5 cm

3 1.05 cm

4 2 cm

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