Question

An optical instrument uses a lens of power 100 D for objective lens and 50 D for its eyepiece. When the tube length is kept at 25 cm. The final image is formed at infinity.

(a) Identify the optical instrument

(b) Calculate the magnification produced by the instrument.

Answer 1

(a) Power of first lens = 100 D

Focal length of first lens

\(f_1 = \frac{1}{P_1} = \frac{1}{100} m = 1 cm\)

Power of second lens = 50 D

Focal length of second lens

\(f_2 = \frac{1}{P_2} = \frac{1}{50}m = 2cm\)

Since focal lengths of lenses are small and focal length of objective is less than focal length of eyepiece and their difference is also small, so it is a compound microscope, with focal length of objective 1 cm and that of eyepiece 2 cm.

(b) When final image formed at infinity.

Magnifying power \(M = - \frac{v_0}{u_0} \left(\frac{D}{f_e}\right)\) 

Length of instrument L = 25 cm.

\(M= \frac{L}{f_0}\left(\frac{D}{f_e}\right)\)

\(= \frac{25}{1} \left(\frac{25}{2}\right)\)

= 312.5