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Introduction to Photonics

Tutorial 1: Ray and Wave Optics

1. A balloon is imaged by a thin bi-convex lens of focal length 10 cm. The balloon is slightly

displaced due to air turbulence. The image is blurred. The screen is adjusted to obtain well

focused image. If the ratio of the change in image distance to the change in object distance is

- 100, calculate the image and object distance before the balloon was displaced.

2.A 65 year old mans eye lens can focus objects from 100 cm to 300 cm. Representing eye

as a simple lens 2 cm from the retina, what is the strength of lens he must wear to focus at 25

cm. Design an anti-reflecting coating for the lens assuming the refractive index of the glass to

be 1.5, and wavelength of light 585 nm (yellow light).

3.

Figure 1: Schematic of a Michelson Interferometer

A Michelson Interferometer could be used in the measurement of two closely spaced

wavelengths. Say we have a sodium lamp emitting two closely spaced wavelengths 5890

and 5896 . The interferometer is first set corresponding to the zero path difference. Near d

= 0, both the fringe patterns will overlap. If mirror is moved away from (or toward) plate

through a distance d, then the maxima corresponding to one wavelength will not, in

general, occur at the same angle as the other . Find the minimum distance d for which the

fringe system dissappears. Find the distance for the mirror to be moved so that the fringesystem appears again.

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4. Obtain the system matrix for a thick lens, and derive the thin lens and thick lens formulas.

5. What should be the thickness of a non-reflecting glass film for a wavelength of 650 nm and

a glass plate of refractive index 1.6. Calculate the refractive index of the thin film. Compare

the reflectivity of crown glass (n= 1.5) with flint glass (n= 1.7) in air. If the refractive index

of the film is 2.4 and the refractive index of glass is 1.5, what is the reflectivity?

6. Consider a lens combination consisting of a convex lens (of focal length +15 cm) and a

concave lens (of focal length 20 cm) separated by 25 cm. Determine the system matrix

elements. For an object (of height 1 cm) placed at a distance of 27.5 cm from the convex lens,

determine the size and position of the image.

Figure 2: System of lenses

6. Use a system of biconvex lenses of focal lengths 20 cm and 7.5 cm to design a

Galileoscope (refracting telescope) that was introduced in class. Discuss the principle of

operation of the Galileoscope and find the system matrix of the device to find the position of

the image for an object located at infinity.

7. A wavelength tuneable Fabry-Perot optical bandpass filter is required for tuning across awavelength band of 100 nm, and it is desired that there should be only one resonant mode of

the filter at a time within the tuning range. Assuming air medium in the cavity, determine the

length of the cavity of the filter. The wavelength resolution of the filter has to be 0.2 nm.

Calculate the Finesse of the cavity and the reflectivity of the mirrors assuming equal

reflectivity for both.

8. The cavity of a He-Ne laser ( = 632 nm) is 20 cm long. The emission spectral range is 1

nm. Find the long mode spacing at the output of the laser. Design a scanning FP-etalon to

study the mode structure of this laser. You should specify:

a) Spacing between the mirrors

b) Reflectivity of the mirrors

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c) Scanning resolution

9. A Michelson interferometer is modified by attaching a piezo-electric transducer to one of

the mirrors M1as shown in the figure.

Figure 3: Michelson interferometer for fringe comparison technique

Light from two lasers were made to traverse the same optical path. The wavelength of

one of the lasers is 632.8 nm. Two similar photo detectors were used to detect the fringe

pattern generated for the two wavelengths. The output of the photo detectors were

amplified and connected to a counter. The piezo electric device transducer voltage is

varied manually from V1= 1 V to V2= 5 V. This resulted in a change in position of the

mirror M1. The counter reading for 632.8 nm is 38 and that of the other wavelength is 45

fringes.

(a)Estimate the wavelength of the other laser.

(b)The voltage of the piezo is increased to 10 V with a displacement of 20 m. Estimate

the distance moved by the mirror.

(c)Calculate the error in wavelength measurement using logarithmic differentiation using

this fringe comparison technique. (Assume the reference wavelength is known with

0.01 nm accuracy and use the above constraint on counter).

(d)Estimate the displacement required for measuring wavelength with an accuracy of

0.001 nm (Assume the reference wavelength is known with 0.0001 nm accuracy). Usereference wavelength as 632.8000 nm. (For wavelengths 612 nm and 543.5 nm).

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10. A fiber optic gyroscope (FOG) is used in rotation sensing, and is based on the principle

of a Sagnac interferometer. Derive the expression for the Sagnac phase shift, and determine

the rate of rotation for which equal intensity will be detected in both arms.

Figure 4: A fiber-optic gyroscope

A FOG used for detecting the Earths rotation is designed by winding a 200 m long fiber on a

10 cm diameter coil. The Sagnac phase shift detected is 36 micro-rad, find the measured

angular rotation of the Earth.