Question

Q61 The ratio of powers of two lenses is 3/4 when they are in contact with each other. Determine the focal lengths of the individual lenses, where one of the lens is
convex and the other is concave.
It is known that the focal length of the combination of the lens is 45 cm.
Ops: A. -12.50 cm and 13 cm
B. 0-15 cm and 11.25 cm
C. -11 cm and 14 cm
D. 0-10 cm and 12 cm​

Answer 1

The values of individual focal lengths are -15 cm and 11.25 cm respectively.

Option (B) is correct.

Explanation:

• Now the ratio between p1 nad p2 = 3: 4
• Put the values.
• f1 / f2 = - p1 / p2
• f1 / f2 = - 3 /4
• f1 = - 3 /4 x f2
• Now total focal length
• 1 / F = 1/f1 + 1/f2
• 1/45 = - 4/3 f2 + 1/f2

Now multiply by 3 on both sides of the equation to simplify it.

1/15 = -4 / f2 + 3 / f2

1/15 = -1 / f2

f2 = - 15

Now  

f1 = - 3/4 x -15

f1 = 11.25 cm