Wave Optics

Some distant star is to be observed by some telescope of diameter of objective lens a, at an angular resolution of 3.0 10-7 radian. If the wavelength of light from the star reaching the telescope is 500 nm, the minimum diameter of the objective lens of the telescope is cm. (nearest integer)

In interference experiment the path difference between two interfering waves at a point A on the screen is /3, where is the wavelength of these waves, and at another point B the path difference is /6. The ratio of intensities at points A and B is .

1. 3
2. 4
3. 1/3
4. 1/4

An unpolarized light of intensity I0 passes through polarizer and then through a certain optically active solution and finally it goes to analyser. If the angle between analyser and polariser is 0° and intensity of light emerged from analyser is 38I0, the angle of rotation of the light by the solution with respect to analyser is degrees.

In a Young double slit experiment, the wavelength of incident light is 6000 Å, the separation between slits S1 and S2 is 5 cm and the distance between slits plane and screen is 50 cm, as shown in the figure below. If the resultant intensity at P is equal to the intensity due to individual slits, the path difference between interfering waves is Å. [figure]

1. 4000
2. 3000
3. 2000
4. 1000

In Young's double slit experiment, the fringe width of the interference pattern produced on the screen is 2.4 μm. If the experiment is carried out in another medium having refractive index 1.2, the fringe width will be μm.

1. 1.2
2. 2
3. 2.4
4. 2.88

The maximum intensity in a Young's double slit experiment is I0. Distance between the slits (d) is 5 , where is the wavelength of light used. The intensity of the fringe, exactly opposite to one of the slits on the screen, placed at D=10d is .

1. I04
2. I02
3. I0
4. 3I04

A slit of width a is illuminated by light of wavelength . The linear separation between 1st and 3rd minima in the diffraction pattern produced on a screen placed at a distance D from the slit system is .

1. D a
2. 1.5 D a
3. 2 D a
4. 3 D a

A telescope with objective diameter R is used to observe a distant star emitting light of wavelength 500 nm, at a resolution of 5 10-7 radian. The value of R is cm.

1. 61
2. 122
3. 244
4. 305

An unpolarized light is incident on the plane interface of air-dielectric medium shown in figure. If the incident angle is equal to Brewster angle, identify the expression representing reflected wave. [figure]

1. (Ex i+Ey j) (kx-kz- t)
2. (Ex i+Ez k) (kx+ky- t)
3. (Ex j+Ey k) (ky+kz- t)
4. (Ex i+Ey j+Ez k) (kx+ky-kz- t)

An unpolarized light of certain intensity passes through a combination of two polarizers whose transmission axes are at 30° and 90°, respectively, with respect to the horizontal axis. A third polarizer with its transmission axis at 60° with the horizontal axis is placed between the two existing polarizers. The ratio of the output intensities with and without the third polarizer is .

1. 3/4
2. 4/3
3. 9/4
4. 4/9

In a double slit experiment, when one of the slits is covered by a transparent mica sheet of refractive index 1.56, the central fringe shifts to the position of 7th bright fringe, obtained with both slits uncovered. If the light source wavelength is 450 nm, the thickness of mica sheet is 10-9 m. The value of is .

In single slit diffraction pattern, the wavelength of light used is 628 nm and slit width is 0.2 mm, the angular width of central maximum is 10-2 degrees. The value of is .

In a Young's double slit experiment, the intensity at some point on the screen is found to be 34 times of the maximum of the interference pattern. The path difference between the interfering waves at this point is x where is wavelength of the incident light. The value of x is .

Given below are two statements : In the light of the above statements, choose the correct answer from the options given below :

1. Both Statement I and Statement II are false
2. Both Statement I and Statement II are true
3. Statement I is true but Statement II is false
4. Statement I is false but Statement II is true

A beam of light consisting of wavelengths 650 nm and 550 nm illuminates the Young's double slits with separation of 2 mm such that the interference fringes are formed on a screen, placed at a distance of 1.2 m from the slits. The least distance of a point from the central maximum, where the bright fringes due to both the wavelengths coincide, is 10-5 m.

An unpolarised light is incident at an interface of two dielectric media having refractive indices of 2 (incident medium) and 2 3 (refracted medium) respectively. To satisfy the condition that reflected and refracted rays are perpendicular to each other, the angle of incidence is

1. 45
2. 60
3. 10
4. 30

In the Young's double slit experiment the intensity produced by each one of the individual slits is Io. The distance between two slits is 2 mm. The distance of screen from slits is 10 m. The wavelength of light is 6000 . The intensity of light on the screen in front of one of the slits is

1. Io2
2. Io
3. 2Io
4. 4Io

In two separate Young's double-slit experimental set-ups and two monochromatic light sources of different wavelengths are used to get fringes of equal width. The ratios of the slits separations and that of the wavelengths of light used are 2 : 1 and 1 : 2 respectively. The corresponding ratio of the distances between the slits and the respective screens (D1/D2) is .

When an unpolarized light falls at a particular angle on a glass plate (placed in air), it is observed that the reflected beam is linearly polarized. The angle of refracted beam with respect to the normal is . ( -1(1.52) = 57.7 , refractive indices of air and glass are 1.00 and 1.52, respectively.)

1. 36.3
2. 39.6
3. 42.6
4. 32.3

Which of the following are true for a single slit diffraction?

1. B, D only
2. A, D only
3. A, C, E only
4. B, C only

In a double slit experiment the distance between the slits is 0.1 cm and the screen is placed at 50 cm from the slits plane. When one slit is covered with a transparent sheet having thickness t and refractive index n (= 1.5), the central fringe shifts by 0.2 cm. The value of t is cm.

1. 6.0 10-3
2. 8 10-4
3. 5.0 10-3
4. 5.6 10-4

Given below are two statements : In the light of the above statements, choose the correct answer from the options given below :

1. Both Statement I and Statement II are true
2. Statement I is true but Statement II is false
3. Statement I is false but Statement II is true
4. Both Statement I and Statement II are false

In a Young's double slit experiment set up, the two slits are kept 0.4 mm apart and screen is placed at 1 m from slits. If a thin transparent sheet of thickness 20 is introduced in front of one of the slits then center bright fringe shifts by 20 mm on the screen. The refractive index of transparent sheet is given by 10, where is .

In a Young's double slit experiment, the source is white light. One of the slits is covered by red filter and another by a green filter. In this case:

1. there shall be alternate interference fringes of red and green.
2. there shall be an interference pattern for red distinct from that for green.
3. there shall be an interference pattern, where each fringe's pattern center is green and outer edges is red.
4. there shall be no interference fringes.

Two plane polarized light waves combine at a certain point whose electric field components are E1 = E0 t E2 = E0 ( t + 3 ) Find the amplitude of the resultant wave.

1. 1.7 E0
2. E0
3. 0.9 E0
4. 3.4 E0

In a Young's double slit experiment, the slits are separated by 0.2 mm. If the slits separation is increased to 0.4 mm, the percentage change of the fringe width is :

1. 25\%
2. 50\%
3. 0\%
4. 100\%

Two polarisers P1 and P2 are placed in such a way that the intensity of the transmitted light will be zero. A third polariser P3 is inserted in between P1 and P2, at particular angle between P2 and P3. The transmitted intensity of the light passing through all three polarisers is maximum. The angle between the polarisers P2 and P3 is :

1. /6
2. 3
3. 4
4. /8

In a Young's double slit experiment, two slits are located 1.5 mm apart. The distance of screen from slits is 2 m and the wavelength of the source is 400 nm. If the 20 maxima of the double slit pattern are contained within the central maximum of the single slit diffraction pattern, then the width of each slit is x 10-3 cm, where x-value is .

Two coherent monochromatic light beams of intensities 4I and 9I are superimposed. The difference between the maximum and minimum intensities in the resulting interference pattern is xI. The value of x is .

Two monochromatic light beams have intensities in the ratio 1:9. An interference pattern is obtained by these beams. The ratio of the intensities of maximum to minimum is

1. 8 : 1
2. 4 : 1
3. 3 : 1
4. 9 : 1