(a) Draw a ray diagram to show image formation when the concave mirror produces a real, inverted and magnified image of the object.

(b) Obtain the mirror formula and write the expression for the linear magnification.

(c) Explain two advantages of a reflecting telescope over a refracting telescope.

OR

(a) Define a wave front. Using Huygens’ principle, verify the laws of reflection at a plane surface.

(b) In a single slit diffraction experiment, the width of the slit is made double the original width. How does this affect the size and intensity of the central diffraction band? Explain.

(c) When a tiny circular obstacle is placed in the path of light from a distant source, a bright spot is seen at the center of the obstacle. Explain why?

(a) Concave mirror produces real, inverted and magnified image for object placed between F and C :

(b) Derivation for mirror formula and magnification: Consider an object AB be placed in front of a concave mirror beyond center of curvature C.

If F is the focus, focal length = f, object distance = u, image distance = v
As $∆$s ABC and A'B'C are similar, 
$\frac{\mathrm{AB}}{{\mathrm{A}}^{\mathrm{\prime }}{\mathrm{B}}^{\mathrm{\prime }}}=\frac{\mathrm{CB}}{{\mathrm{CB}}^{\mathrm{\prime }}}$         ......(i)
Again, as $∆$s ABP and A'B'P are similar,
$\begin{array}{r}\frac{\mathrm{AB}}{{\mathrm{A}}^{\mathrm{\prime }}{\mathrm{B}}^{\mathrm{\prime }}}=\frac{\mathrm{PB}}{{\mathrm{B}}^{\mathrm{\prime }}\mathrm{P}}\\ \Rightarrow \frac{\mathrm{CB}}{{\mathrm{CB}}^{\mathrm{\prime }}}=\frac{\mathrm{PB}}{{\mathrm{PB}}^{\mathrm{\prime }}}\end{array}$    ......(ii)
                                         ......(iii)
            $\begin{array}{l}\therefore \text{ From (iii), }\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\frac{\mathrm{PB}-\mathrm{PC}}{\mathrm{PC}-{\mathrm{PB}}^{\mathrm{\prime }}}=\frac{\mathrm{PB}}{{\mathrm{PB}}^{\mathrm{\prime }}}\\ \Rightarrow \hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\frac{-\mathrm{u}+\mathrm{R}}{-\mathrm{R}+\mathrm{v}}=\frac{-\mathrm{u}}{\mathrm{v}}\end{array}$
$\begin{array}{l}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}[\because \mathrm{PB}=-\mathrm{u},\mathrm{PC}=-\mathrm{R},\\ \Rightarrow \hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\mathrm{uPB}=-\mathrm{v}]\\ \Rightarrow \hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\frac{1}{\mathrm{v}}+\frac{1}{\mathrm{u}}=\frac{2}{\mathrm{R}}\\ \Rightarrow \hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\frac{1}{\mathrm{v}}+\frac{1}{\mathrm{u}}=\frac{1}{\mathrm{f}}(\because \mathrm{R}=2\mathrm{f})\end{array}$
Linear magnification, m=$\frac{\mathrm{Image} \mathrm{height}\left({\mathrm{h}}_{\mathrm{i}}\right)}{\mathrm{Object} \mathrm{height}\left({\mathrm{h}}_0\right)}$
 $\text{ From equation (ii), }\frac{{\mathrm{A}}^{\mathrm{\prime }}{\mathrm{B}}^{\mathrm{\prime }}}{\mathrm{AB}}=\frac{{\mathrm{PB}}^{\mathrm{\prime }}}{\mathrm{PB}}$
Using new Cartesian sign conventions, $\mathrm{A}\text{'}\mathrm{B}\text{'}$
$=-{\mathrm{h}}_{2^{\mathrm{\prime }}}\mathrm{AB}=+{\mathrm{h}}_{1^{\mathrm{\prime }}}{\mathrm{PB}}^{\mathrm{\prime }}=-\mathrm{v},\mathrm{PB}=-\mathrm{u}$
$\begin{array}{l}\therefore \hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\frac{-{\mathrm{h}}_2}{{\mathrm{h}}_1}=\frac{-\mathrm{v}}{\mathrm{u}}=\frac{\mathrm{v}}{\mathrm{u}}\\ \text{ or }\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\mathrm{m}=\frac{{\mathrm{h}}_2}{{\mathrm{h}}_1}=\frac{-\mathrm{v}}{\mathrm{u}}\end{array}$
(c) Advantages of reflecting telescope over a refracting telescope are :

1. Reflecting telescope is free from chromatic and spherical aberrations unlike refracting telescope.

Thus image formed is sharp and bright.
2. It has a larger light gathering power so that a bright image of even far off object is obtained.
3. Resolving power of reflecting telescope is large.