Question

А сonvex lens is in contact with concave lens. The magnitude of the ratio of their powers is `2/3`. Their equivalent focal length is 30 cm. What are their individual focal lengths (in cm)?

Options

• −15, 10

• −10, 15

• 75, 50

• −75, 50

Answer 1

−15, 10

Explanation:

Given: Focal length = 30 cm

Convex lens power = P₁ (positive)

Concave lens power = P₂ (negative)

`|(P_1)/(P_2)| = 2/3`

`P_1 = 2/3|P_2|`

P₂ = −x

`P_1 = 2/3 x`

P_eq = P₁ + P₂

`P_(eq) = 1/30`

`2/3 x - x = 1/30`

`-1/3 x = 1/30`

x = `-1/10`

`P_2 = -x  = 1/10`

`P_1= 2/3 x = -1/15`