As shown in the figure, a combination of a thin plano-concave lens and a thin plano-convex lens is used to image an object placed at infinity. The radius of curvature of both the lenses is 30 cm and r

Question

As shown in the figure, a combination of a thin plano-concave lens and a thin plano-convex lens is used to image an object placed at infinity. The radius of curvature of both the lenses is $30 cm$ and refraction index of the material for both the lenses is $1.75$ . Both the lenses are placed at distance of $40 cm$ from each other. Due to the combination, the image of the object is formed at distance $x =$ ______ $cm$ , from concave lens.

TestHub · Accepted Answer

Using Lens Makers formula for the plano-concave part, we can write

$\frac{1}{f_{1}} = (1.75 - 1) (- \frac{1}{30})$

$\Rightarrow f_{1} = - 40 cm$

Using Lens Makers formula for the plano-convex part, we can write

$\frac{1}{f_{2}} = (1.75 - 1) (\frac{1}{30}) \Rightarrow f_{2} = 40 cm$

Image from first lens will be virtual and on the left of first lens at focal length $40 cm$ . So the object for second lens will be $80 cm$ from second lens which is $2 f_{2}$ . Final image is formed at $80 cm$ from second lens on the right.
So, $x = 120$ .

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