A window is in the form of a rectangle surmounted by a semicircular opening. The total perimeter of the window is 10 m. Find the dimensions of the window to admit maximum light through the whole opening.

A window of perimeter P (including the base of the arch) is in the form of a rectangle surrounded by a semi-circle. The semi-circular portion is fitted with the colored glass while the rectangular part is fitted with the clear glass that transmits three times as much light per square meter as the colored glass does. What is the ratio for the sides of the rectangle so that the window transmits the maximum light?

A sheet of area 40m^2 is used to make an open tank with square base. Find the dimensions of the base such that the volume of this tank is maximum.

A fraunhofer diffraction pattern is formed by a light,of wavelength 600nm, through a slit if width 1.2 mu m . Find the angular position of the first minimum and angular width of the central maximum.

A ladder of length 10m just touches a window 8 m high from the ground on a wall. Find the distance between the foot of the ladder from the wall.

Find the area of four walls of a room (Assume that there are no doors or windows ) if its length 12m. Breadth 10 m. and height 7.5 m.

A fraunhofer diffraction pattern is being formed by light wave of frequency 5xx 10^(14) Hz through a slit of width 10^(-2) m . Find the angular width of central maximum [Velocity of light in vacuum = 3xx10^(8) m. s^(-1) ]

A parallel light beam of wavelength 6000Å passes through a slit 0.2 mm wide and forms a diffraction pattern on a screen 1.0 m away from the slit. Find the width of the central maximum in mm on the screen.

In Young's double slit experiment the coherent sources are 1.5 mm apart and the fringes are obtained on a screen at a distance 2.5 m from the plane of the sources. If the sources is illuminated with a light of 589.3 nm wavelength , find the number of fringes in the interference pattern thus formed on the screen. Total length of the fringes are 4.9 xx 10 ^(-3) m.