Question

In a compound microscope, the focal lengths of two lenses are 1.5 cm and 6.25 cm an object is placed at 2 cm from objective and the final image is formed at 25 cm from eye lens. The distance between the two lenses is ______.

Options

• 6.00 cm

• 7.75 cm

• 9.25 cm

• 11.00 cm

Answer 1

In a compound microscope, the focal lengths of two lenses are 1.5 cm and 6.25 cm an object is placed at 2 cm from objective and the final image is formed at 25 cm from eye lens. The distance between the two lenses is 11.00 cm.

Explanation:

f_o = 1.5 cm, f_e = 6.25 cm, u_o = - 2 cm, v_e = - D = - 25 cm

By objective lens `1/"f"_"o" = 1/"v"_"o" - 1/"u"_"o"`

`1/1.5 = 1/"v"_"o" - 1/(-2) => 1/"v"_"o" = 1/1.5 - 1/2` or v_o = 6 cm

By eye piece `1/"f"_"e" = 1/"v"_"e" - 1/"u"_"e"`

`1/6.25 = 1/(- 25) - 1/(- "u"_"e")`

`=> 1/"u"_"e" = 1/6.25 + 1/25 = 4/25 + 1/25 = 1/5`

ue = 5 cm, Length of tube = L = v_o + u_e

= 6.0 cm + 5.0 cm, L = 11 cm