A lady cannot see objects closer than 40 cm from the left eye and closer than 100 cm from the right eye. While on a mountaineering trip, she is lost from her team. She tries to make an astronomical telescope from her reading glasses to look for her teammates. (A) Which glass should she uses as the eyepiece? (B) What magnification can she get with relaxed eye?

Given data

For the left glass lens –

The lady cannot see objects closer than 40cm, v = – 40 cm

Least distance of clear vision, u = – 25 cm

Using lens formula –

Substituting the values-

Hence, the focal length of the left eye glass lens is 66.6 cm

For the right eye glass –

The lady cannot see objects closer than 40cm, v = – 100 cm

Least distance of clear vision, u = – 25 cm

Using lens formula –

Substituting the values-

Hence, the focal length of the right eye glass lens is 33.3 cm

(a) There are two lenses present in astronomical telescope, the objective and eyepiece lens.

The objective lens have a large focal length and the eyepiece lens have a smaller focal length.

The lady uses glasses with right lens of focal length 33.33 and left sides eye lens of focal length 66.66

So, she should use the left eye lens as objective and right lens as the eyepiece lens.

(b) When eyes are relaxed and microscope is used in normal adjustment, then the objective

focal length and eyepiece focal length of the microscope becomes-

f_o = 66.6 cm and f_e = 33.3 cm

Magnification m, for normal adjustment -

So, when eyes are relaxed, she can get the magnified image of the object up to 2D