Solution:

Ans. Magnifying power is defined as the angle subtended by the image to the angle subtended (at the unaided eye) by the object.

(Alternatively : Also accept this definition in the form of formula)

$$m=m_0\times m_e=\frac{L}{f_0}\times \frac{D}{f_e}$$

To increase the magnifying power both the objective and eyepiece must have short focal lengths $($ as $m=\frac{L}{f_o}\times \frac{D}{f_e})$ $1/2+1/2$

[CBSE Marking Scheme 2017]

Commonly Made Error

• Students wrote correct definition of magnifying power of the microscope but wrote wrong formula.

[AI Q. 3. (i) State the condition under which a large magnification can be achieved in an astronomical telescope.

(ii) Give two reasons to explain why a reflecting telescope is preferred over a refracting telescope.

U[CBSE 2017, Foreign set]

Ans. (i)

$$m=\frac{f_0}{f_e}$$

By increasing $f_o$ or decreasing $f_e$

(ii) (a) No chromatic aberration.

(b) No spherical aberration.

(c) Mechanical advantage - low weight, easier to support.

(d) Mirrors are easy to prepare.

(e) More economical.

(Any two) $1/2+1/2$

[CBSE Marking Scheme 2017] AT Q. 4. You are given two converging lens of focal lengths $1.25\mathrm{cm}$ and $5\mathrm{cm}$ to design a compound microscope. If it is desired to have a magnification of 30, find out the separation between the objective and the eyepiece.

A [OD 2015]

Ans. Given, $f_o=1.25\mathrm{cm},f_e=5\mathrm{cm}$

Magnification, $m=30$,

If we set these lens for minimum distance for distinct vision, then for

$$\begin{array}{}\text{(1)}& m& =\frac{L}{f_o}(1+\frac{D}{f_e})m& =30\mathrm{L}& =6.25\mathrm{cm}\end{array}$$

Hence, distance between two lenses is

$$\begin{array}{rlrl}& =f_o+6.25+f_e& =(1.25+6.25+5.0)\mathrm{cm}& =12.5\mathrm{cm}\end{array}$$

This is a required separation between the objective and the eyepiece. [AI Q. 1. Draw a labelled ray diagram to show the image formation in a refracting type astronomical telescope in the normal adjustment position. Write two drawbacks of refracting type telescopes.

A [CBSE SQP 2018-19]

Drawbacks :

(i) Large sized lenses area heavy and difficult to support.

(ii) Large sized lenses suffer from chromatic and spherical aberration.

[CBSE Marking Scheme 2018]