Derive mirror equation for a convex mirror. Using it, show that a convex mirror always produces a virtual image, independent of the location of object.

OR

(a) Draw a ray diagram for final image formed at distance of distinct vision (D) by a compound microscope and write expression for its magnifying power.

b) An angular magnification (magnifying power) of 30x is desired for a compound microscope using as objective of focal length 1.25cm and eye piece of focal length 5cm. How will you set up the compound microscope?

Let us consider the convex mirror of focal length = f

The object is placed on principle axis.

Distance between object and the mirror= u

The distance between the image and the mirror = v

Using the ray diagram

Similarly,

But DE=AB and when the aperture of the mirror is very small then EF= PF

Hence, equation (ii) becomes

By looking at the diagram, PF= f; PB₁=v; PB = u, PC= 2f, therefore,

Dividing the above equation (4) by uvf, we get

For a convex mirror: focal length f is always positive

∴ f >0

Since the object is on the left of the convex mirror, u<0

Using the above formula, we can conclude that v is positive if the image is at the back of the mirror. Therefore, the image is virtual whatever be the value of u.

OR

The magnification of the microscope is given by m= m_om_e where, m_o is the magnification due to objective lens and m_e is the magnification due to eyepiece of microscope.

Magnification of objective lens

Magnification of eyepiece

b) Given: angular magnification = 30

Focal length of eyepiece f_e = 5cm

Focal length of objective f_o = 1.25 cm

The image formed at least distance of vision= d= 25cm

Magnification of eyepiece m_e=

Magnification of objective m_o = m/ m_e

Now using, lens makers formula,

Again, using lens maker’s formula for eyepiece,

The distance between object and eyepiece = 4.17 cm

Separation between the objective and eyepiece= 4.17+7.5 = 11.67 cm