Question

The focal lengths of the objective and the eyepiece of a compound microscope are 1 cm and 2 cm respectively. If the tube length of the microscope is 10 cm, the magnification obtained by the microscope for most suitable viewing by relaxed eye is ______.

Options

• 250

• 200

• 150

• 125

Answer 1

The focal lengths of the objective and the eyepiece of a compound microscope are 1 cm and 2 cm respectively. If the tube length of the microscope is 10 cm, the magnification obtained by the microscope for most suitable viewing by relaxed eye is 125.

Explanation:

For the eyepiece:

`1/f_e = 1/v_e - 1/u_e`

⇒ `1/2 = 1/(-25) - 1/u_e`

⇒ u_e = −1.85 cm

Since the length of pipe is 10 cm.

So, |v₀| + |u_e| = 10 cm

⇒ |v₀| = 10 + (−1.85) = 8.15 cm

For the objective lens:

`1/f_0 = 1/v_0 - 1/u_0`

⇒ `1/1 = 1/8.15 - 1/u_0`

⇒ u₀ = −0.877 cm

Now, magnification,

`m = v_0/|u_0|(1 + D/f_e)`

`m = 8.15/0.877(1 + 25/2)`

m = 125.46 ≃ 125