Question

Two lenses, one convex and another concave, of the focal lengths 10 cm and 20 cm respectively are taken together and used as a single lens. If a point object is held at a distance of 20 cm from the compound lens, find the position of its image.

• A. At infinity
• B. At focus of combined lens
• C. none of the above
• D. At 2x focal distance of combined lens

Answer 1

Answer: (A)

$f_1=10cm;f_2=-20cm$

we know,

$\frac{1}{f}=\frac{1}{f_1}+\frac{1}{f_2}$

$\frac{1}{f}=\frac{1}{10}-\frac{1}{20}$

$f=20cm$

this indicates that the lens is converging.

given: $u=-20cm$

$\frac{1}{f}=\frac{1}{v}-\frac{1}{u}$

$\frac{1}{v}=\frac{1}{f}+\frac{1}{u}$

$\frac{1}{v}=\frac{1}{20}-\frac{1}{20}$

$v=infinity$

hence,image will be formed at infinity.