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)

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 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 .

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.

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 .

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, 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 .

If the measured angular separation between the second minimum to the left of the central maximum and the third minimum to the right of the central maximum is 30 in a single slit diffraction pattern recorded using 628 nm light, then the width of the slit is .

A double slit interference experiment performed with a light of wavelength 600 nm forms an interference fringe pattern on a screen with 10th bright fringe having its centre at a distance of 10 mm from the central maximum. Distance of the centre of the same 10th bright fringe from the central maximum when the source of light is replaced by another source of wavelength 660 nm would be mm.

A thin transparent film with refractive index 1.4, is held on circular ring of radius 1.8 cm. The fluid in the film evaporates such that transmission through the film at wavelength 560 nm goes to a minimum every 12 seconds. Assuming that the film is flat on its two sides, the rate of evaporation is 10-13 m3/s.

In a Young's double slit experiment, the intensity at a point is ( 14 )th of the maximum intensity, the minimum distance of the point from the central maximum is . (Given : = 600 nm, d = 1.0 mm, D = 1.0 m)

Monochromatic light of wavelength 500 nm is used in Young's double slit experiment. An interference pattern is obtained on a screen. When one of the slits is covered with a very thin glass plate (refractive index = 1.5), the central maximum is shifted to a position previously occupied by the 4th bright fringe. The thickness of the glass-plate is .

A parallel beam of monochromatic light of wavelength 600 nm passes through single slit of 0.4 mm width. Angular divergence corresponding to second order minima would be 10-3 rad.

Two slits are 1 mm apart and the screen is located 1 m away from the slits. A light of wavelength 500 nm is used. The width of each slit to obtain 10 maxima of the double slit pattern within the central maximum of the single slit pattern is 10-4 m.

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

In Young's double slit experiment, carried out with light of wavelength 5000 Å, the distance between the slits is 0.3 mm and the screen is at 200 cm from the slits. The central maximum is at x = 0 cm. The value of x for third maxima is mm.

In a single slit experiment, a parallel beam of green light of wavelength 550 nm passes through a slit of width 0.20 mm. The transmitted light is collected on a screen 100 cm away. The distance of first order minima from the central maximum will be x 10-5 m. The value of x is :

Two wavelengths 1 and 2 are used in Young's double slit experiment. 1=450 nm and 2=650 nm. The minimum order of fringe produced by 2 which overlaps with the fringe produced by 1 is n. The value of n is .

In Young's double slit experiment, monochromatic light of wavelength 5000 Å is used. The slits are 1.0 mm apart and screen is placed at 1.0 m away from slits. The distance from the centre of the screen where intensity becomes half of the maximum intensity for the first time is 10-6 m.

Two waves of intensity ratio 1:9 cross each other at a point. The resultant intensities at that point, when (a) Waves are incoherent is I1 (b) Waves are coherent is I2 and differ in phase by 60 . If I1I2= 10x then x= .

In a double slit experiment shown in figure, when light of wavelength 400 nm is used, dark fringe is observed at P. If D=0.2 m, the minimum distance between the slits S1 and S2 is mm. [figure]

In a single slit diffraction pattern, a light of wavelength 6000 A is used. The distance between the first and third minima in the diffraction pattern is found to be 3 mm when the screen is placed 50 cm away from slits. The width of the slit is 10-4 m.

A parallel beam of monochromatic light of wavelength 5000 Å is incident normally on a single narrow slit of width 0.001 mm. The light is focused by convex lens on screen, placed on its focal plane. The first minima will be formed for the angle of diffraction of (degree).