BE Mechanical Engineering छमाही २ (इंजीनियरिंग) - University of Mumbai Important Questions

Change the order of integration and evaluate `int_0^2 int_(2-sqrt(4-y^2))^(2+sqrt(4-y^2)) dxdy` 

Find by double integration the area bounded by the parabola 𝒚𝟐=𝟒𝒙 And 𝒚=𝟐𝒙−𝟒 

Find the volume bounded by the paraboloid 𝒙^𝟐+𝒚^𝟐=𝒂𝒛 and the cylinder 𝒙^𝟐+𝒚^𝟐=𝒂^𝟐. 

Change to polar coordinates and evaluate `int_0^1 int_0^x (x+y)dydx` 

Why the Newton’s rings are circular and centre of interference pattern (reflected) is dark?

What is Rayleigh’s criterion of resolution? Define resolving power of grating?

What will be the fringe pattern if wedge shaped air film is illuminated with white light?

Obtain the condition for maxima and minima of the light reflected from a thin transparent film of uniform thickness. Why is the visibility of the fringe much higher in the reflected system than in the transmitted system.

Explain the experimental method to determine the wavelength of spectral lines using grating. A diffraction grating has 5000 lines / cm and the total ruled with is 5cm. Calculate dispersion for a wavelength of 5000 A0 in the second order.

A wedge shaped air film having angle 40 seconds is illuminated by monochromatic light. Fringes are observed vertically through a microscope. The distance between 10 consecutive dark fringes is 1.2 cm. find the wavelength of monochromatic light used.

Describe in detail the concept of anti-reflecting film with a proper ray diagram.

Why the Newton’s rings are circular and fringes in wedge shaped film are straight? 

What is grating and grating element? 

What is meant by thin film? Comment on the colours in thin film in sunlight.

Derive the conditions of maxima and minima due to interference of light transmitted from thin film of uniform thickness.

Explain the experimental method to determine the wavelength of spectral line using diffraction grating.
What is the highest order spectrum which can be seen with monochromatic light of wavelength 6000 A^o by means of a diffraction grating with 5000 lines/cm?

With Newton’s ring experiment explain how to determine the refractive index of liquid. 

Explain how interference in wedge shaped film is used to test optical flatness of given glass plate.

What is diffraction grating? What is the advantage of increasing the number of lines in the grating? 

In Newtons’s ring experiment,what will be the order of dark ring which will have double the diameter of 40th dark ring?