## Ray Optics

**(Important Theory Questions)**

**1**. Derive mirror formula for a concave mirror and convex mirror.

**2**. Derive an expression for lateral shift and normal shift. On what factors these depend.

**3**. Define TIR and write the conditions for TIR. Derive a relation between critical angle and the refractive index of the medium. Also explain the working of isosceles prism and optical fiber.

**4**. Derive the following relation for a real image formed by a convex refracting surface when the object is placed in rarer medium. Also write the assumptions and sign convention used.

μ₂ / v - μ₁/u = (μ₂ - μ₁) / R

**5**. Derive the lens maker’s formula. Also write the assumptions and sign convention used.

**6**. Derive the lens formula for convex lend and concave lens.

**7**. Derive the relation for equivalent focal length or power when two thin lenses are placed in contact to each other. In which condition the lens combination will act as a plane glass sheet.

**8**. Derive the following relations for a prism:

Where the symbols have their usual meanings.

**9**. Draw a ray diagram to show the image formation in refracting type astronomical telescope in the near point adjustment (when image is formed at LDDV i.e. D=25cm). Derive an expression for its magnifying power. Why the diameter of objective of telescope should be large.

**10**. Draw a ray diagram to show the image formation in refracting type astronomical telescope in the normal adjustment (when image is formed at infinity). Derive an expression for its magnifying power. How does the magnifying power get affected on increasing the aperture of the objective lens and why?

**11**. Draw a ray diagram to show the image formation a compound microscope. Explain briefly the working. Derive an expression for its magnifying power. Why the diameter of objective of microscope should be small.

**12**. Draw a labeled diagram of a reflecting type telescope. State two advantages of this telescope over refracting type telescope.

**13**. Define resolving power of compound microscope. How does the resolving power of a compound microscope change when-

(a) Refractive index of medium between the object and objective lens increases

(b) Wavelength of the light used is increased

(c) decreasing the diameter of objective

(d) increasing the focal length of its objective.

**14**. Define the resolving power of astronomical telescope. Write the expression for it and state, on what factors it depends