Wave Optics

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