Answer to Question #140595 in Optics for sharfa

Question

An object ‘o’ , a converging lens L of focal length 15 cm and concave mirror M are placed.the object distance is 30 cm, while the distance between lens 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

Solution. According to the condition of the problem, the object is in front of a concave lens with a focal length of 15 cm at a distance of 30 cm from it. Using formula

$$\frac{1}{f}=\frac{1}{d_o}+\frac{1}{d_i}$$

where d₀ is distance to object; d_i is distance to image. Therefore

$$d_i=\frac{f\times d_0}{d_0-f}=\frac{15\times 30}{30-15}=30cm$$

Since the distance from the lens to the mirror is 50 cm, hence the distance from the image of the object created by the lens and the mirror is equal

$$d=50-30=20cm$$

Using the formula for the mirror

$$\frac{1}{f}=\frac{1}{d_o}+\frac{1}{d_i}$$

Get according to the condition of the problem d₀=d=20cm and d_i=-(50+30)=-80cm (given the location of the image). As result

$$f=\frac{-80\times 20}{80-20}=-26.6 cm$$

In this case, the closest answer is 25 cm, given that the distance is positive.

Answer. (4) 25cm.