Answer to Question #140433 in Optics for sharfa

Question

12. An object ‘o’ , a converging lens L of focal length 15 cm where object distance is 30 cm and concave mirror M are placed. the distance between o and mirror is 50 cm. If the object and the final image coincide , the focal length of M is ( 1 ) 10 cm ( 2 ) 15 cm ( 3 ) 20 cm ( 4 ) 25 cm ( 5 ) 30 cm

Answer 1

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

$\frac{1}{15} = \frac{1}{v}+\frac{1}{30}$

$\frac{1}{v} = \frac{1}{15} + \frac{1}{30} = \frac{1}{10}$

v = 10 cm

d = v +2f

50 = 10 + 2f

40 = 2f

f = 20 cm

Answer: (3) 20 cm