Optics Answers

The radius of the fifth zone of a zone plate is 2 mm. Considering the zone plate as

a converging lens, calculate its focal length for light of wavelength 4800 Å.

The Fraunhofer diffraction pattern due to a single slit of width 0.4 cm is obtained

with the help of a lens of focal length 30 cm. If the wavelength of light used is

5890 Å, calculate the distance of the first dark fringe and the consecutive bright

fringe from the axis.

What is a zone plate? How does a positive zone plate differ from a negative zone

plate? Show that each Fresnel zone has nearly the same area.

Explain how Michelson interferometer is used to determine the refractive index of a

thin plate.

Newton’s rings are formed in reflected light of wavelength 5890 *10^8cm with a

liquid between the plane and curved surfaces. The diameter of the fifth ring is

0.3 cm and the radius of curvature of the curved surface is 100 cm. Calculate

the refractive index of the liquid, when the ring is bright.

Distinguish between fringes of equal inclination and fringes of equal thickness

Derive an expression for the displacement of the nth bright fringe in Young’s

double-slit experiment when a thin transparent plate of refractive index  and

thickness t is introduced in the path of one of the constituent interfering beams of

light. Will there be any change in the fringe-width after the introduction of the

plate?

The electric field vectors of two light waves propagating along the positive zdirection

are given as

E₁(z,t) = xˆ E₀₁cos(kz - (omega)t)

E₂(z,t) = yˆ E₀₂cos(kz-(omega)t + (si))

where xˆ and yˆ are unit vectors along x and y-axes, respectively. Show that when

these two waves superpose, we obtain elliptically polarised light. Also show that

the linear and circular polarisations are special cases of elliptical polarisation

Determine the frequencies of the fundamental mode and the next two harmonics

that can be set up on a sitar string of length 1.0 m. Take the speed of waves of the

string to be 2.8 *10³ms^-1.

The mathematical expression for one dimensional wave travelling along the

positive x-direction is given as

y(x,t ) * 0.02 sin (42 x *1886t )m

where x is in meters and t is in seconds. Determine the direction of propagation of

the wave and calculate its amplitude, wavelength, frequency and velocity.