Find the intensity at a point on a screen in Young's double-slit experiment where the interfering waves of equal intensity have a path difference.
\(\text { (i) } \frac{\lambda}{4} \text {, and (ii) } \frac{\lambda}{3}\)

The critical angle for a given piece of glass is 45°. Calculate the polarising angle for it. Also calculate the angle of refraction when light is incident on this glass at an angle of incident equal to i_p.

You are given two converging lenses of focal lengths 1.25 cm and 5 cm to design a compound microscope. If it is desired to have a magnification of 30, find out the separation between the objective and the eyepiece.

The total magnification produced by a compound microscope is 20. The magnification produced by the eyepiece is 5. The microscope is focused on a certain object. The distance between the objective and eyepiece is observed to be 14 cm. If the least distance of distinct vision is 20 cm, calculate the focal length of the objective and the eyepiece.

A small telescope has an objective lens of focal length 150 cm and an eyepiece of focal length of 5 cm. What is the magnifying power of the telescope for viewing the distant objects in normal adjustment?
If this telescope is used to view a 100 m tall tower 3km away, what is the height of the image of the tower formed by the objective lens?

In young's double slit experiment, the angular width of a fringe is found to be 0.2^o on a screen placed 1m away. The wavelength of light used is 600 nm. What will be the angular width of the fringe if the entire experimental apparatus is immersed in water? Take refractive index of water as \(\cfrac { 4 }{ 3 } \).

A Parallel beam of light of 500 nm falls on a narrow slit and be resulting diffraction pattern is observed on a screen 1m away. It is observed that the first minimum is at a distance of 2.5 mm from the centre of the screen. Calculate the width of the slit.

If the focal lengths of the objective and eyepiece of a microscope are 2 cm and 5 cm and 5 cm respectively and the distance between them is 20 cm, what is the distance of the object from the objective when the image seen by the eye is 25 cm from eyepiece? Also find the magnifying power.

An optical instrument used for angular magnification has a 25 D objective and a 20D eyepiece. The tube length is 25 cm when the eye is least strained. (a) Whether it is a microscope or a telescope? (b) What is the angular magnification produced?

In Young's experiment, the upper slit is covered by a thin glass plate of refractive index 1.4 while the lower slit is covered by another glass plate having the same thickness as the first one but having refractive index 1.7. Interference pattern is observed using light of wavelength 5400 Å. It is observed that the point P on the screen where the central maximum (n = 0) fell before the glass were inserted now has \(\cfrac { 3 }{ 4 } \) th original intensity. It is further observed that what used to be the fifth maximum earlier, lies below the point P while the sixth minimum lies above P. Calculate the thickness of the glass plate.

The eyepiece and objective of a microscope having focal lengths of 0.03 m and 0.04 m respectively are separated by a distance 0.2 m. Now the eyepiece and the objective are to be interchanged such that the angular magnification of the instrument remains the same. What is the separation between the lenses?

In double-slit experiment, SS₂ is greater than SSI by 0.25 A. Calculate the path difference between two interfering beams from S₁ and S₂ for minima and maxima on the screen.

Two polaroids are set in crossed positions. A third polaroid is placed between the two making an angle e with the pass axis of the first polaroid. Write the expression for the intensity of light transmitted from the second polaroid. In what orientations will the transmitted intensity be
(i) minimum and
(ii) maximum.

If a particle is thrown horizontally at a speed of 3 x 10⁸ms^-1, deduce the verticalfall in traveling 1 km distance. Given: g = 10 ms^-2, Does that result depend upon the mass of the particle? Comment on your result, considering that Newton thought light is made up of corpuscles that at a very large speed by the source 

Light of wavelength 5000 Å falls on a plane reflecting surface. What are the wavelength and frequency of reflected light? For what angle of incidence is the reflected ray normal to the incident ray?