Question

A concave lens and a convex lens are placed touching each other. The ratio of magnitudes of their powers is 2:3. The focal length of the system is 30cm. Then the focal lengths of individual lenses are

(a) -75 cm,50 cm
(b) - 15 cm, 10 cm
(c) 75 cm,50 cm
(d) 75 cm, -50 cm

(explain how you got the answer please. don't just choose an option. thank you )​

Answer 1

The answer is b (-15cm and,10cm)

Explanation:

as given in the question

P1/P2=-2/3

as we know that the focus is reciprocal of power

so F1=1/P1 and F2 = 1/P2 npe we put this value in P1/P2

we get F2/F1=2/3

F2=-2/3F1...

now we take f equovalwy we get

1/F1+1/F2=1F(equivalent)

putting these value we get

1/F1+(-3/2f1)=1/30...

1/F1-3/2F1=1/30

-1/2F1=1/30

F1=-30/2=-15cm...

for F2 it will be -2/3F1

=-2/3×(-15)=10cm

so focal lengt of lens are F1=-15cm and F2 is 10 cm...