Question

A convex lens A of focal length 20 cm and a concave lens B of focal length 5 cm are kept along the same axis with a distance d between them. If a parallel beam of light falling on A leaves B as a parallel beam, then the distance d in cm will be

A. 25 B. 15 C. 30 D. 50

Answer 1

According to the question following is the ray diagram.

As the incident ray is parallel to the principal axis. Therefore in absence of concave lens it will form an image at focus of convex lens. 

∴ v = 20cm = f 

Distance of Image I from the concave lens B will be = u = 20 – d 

Now, the image I will act as object for the concave lens. 

Since image object (image I) is at focus of concave lens. Therefore, Image will be formed at infinity

⇒ v = ∞

Focal length = -5cm. 

By Lens Formula.

\(\frac1v-\frac1u=\frac1f\)

⇒ \(\frac1{∞}-\frac1{20-d}=\frac1{-5}\)

⇒ 0 - \(\frac1{20-d}=\frac1{-5}\)

⇒ \(\frac1{20-d}=\frac1{5}\)

⇒ 20 - d = 5

⇒ d = 20 - 5 = 15 cm.

Therefore, the distance d will be 15cm. 

Hence the option B is correct