Question

A concave lens of focal length 40 cm is coaxially in contact with two convex lenses, each of focal length 20 cm, on each side. The focal length of the combination is ______.

Options

• zero

• `20/3` cm

• `-20/3` cm

• `40/3` cm

Answer 1

A concave lens of focal length 40 cm is coaxially in contact with two convex lenses, each of focal length 20 cm, on each side. The focal length of the combination is `bbunderline(40/3 cm)`.

Explanation:

Given: Two convex lenses: f₁ = f₃ = +20 cm

One concave lens: f₂ = −40 cm

By using the lens combination formula:

`1/F = sum 1/f_i`

= `1/20 + 1/20 - 1/40`

= `2/20 - 1/40`

= `4/40 - 1/40`

= `(4 - 1)/40`

`1/F = 3/40`

F = `40/3` cm