In the following diagram focal length of convex lens is 20 cm. What is the focal length of concave lens?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 30 cm
The convex lens alone would form its image at I, 20 cm behind it. The concave lens is 5 cm behind the convex lens, so I lies \( 20-5 = 15\,\mathrm{cm} \) beyond the concave lens: it is a virtual object for the concave lens. The final image \( I_1 \) is 30 cm beyond the concave lens.
Take distances from the concave lens, positive in the direction of the light: \( u = +15\,\mathrm{cm} \) (virtual object), \( v = +30\,\mathrm{cm} \). Use the lens formula \( \frac{1}{v}-\frac{1}{u} = \frac{1}{f} \).
\( \displaystyle \frac{1}{f} = \frac{1}{30}-\frac{1}{15} = -\frac{1}{30}\,\mathrm{cm^{-1}} \)
\( f = -30\,\mathrm{cm} \)
The negative sign shows a diverging lens, so the focal length of the concave lens is 30 cm.