Two polaroids `P_(1) and P(2)` are placed with pass axes perpendicular to each other. Unpolarised light of intensity `I_(0)` is incident on `P_(1)`. A thrid polaroid `P_(3)` is kept in between `P_(1) and P_(2)` such that its pass axis makes an angle of `45^(@)` with that of `P_(1)`. Determine the intensity of light transmitted through `P_(1) , P_(2) "and" P_(3).`

A narrow beam of unpolarised light of intensity I_(0) is incident on a polaroid P_(1) . The light transmitted by it is then incident on a second polaroid P_(2) with its pass axis making angle 60^(@) relative to the pass axis of P_(1) . Find the intensity of the light transmitted by P_(2) .

The optic axes of two polaroids are inclined at an angle of 45@ with each other. Unpolarised light of intensity I_0 being incident on the first polaroid emerges from the second polaroid. Find the intesity of the emergent light.

The optic axis of two polaroids are inclined at an angle of 45^(@) with each other. Unpolarised light of intensity I_(0) being incident on the first polaroid emerges from the second polaroid. Find the intensity of the emergent light.

The lines p(p^2+1)x-y+q=0 and (p^2+1)^2x+(p^2+1)y+2q=0 are perpendicular to a common line for

A straight line passes through P (1,2) and is such that its intercept between the axes is bisected at P. Then the equation of the line is-

Two glass prisms P_(1) and P_(2) are to be combined together to produce dispersion without deviation. The angles of the prisms P_(1) and P_(2) are selected as 4^(@) and 3^(@) respectively. If the refractive index of prism P_(1) is 1.54, then that of P_(2) will be

P_(1) and P_(2) are the lengths of the perpendicular from the foci on the tangent of the ellipse and P_(3) and P_(4) are perpendiculars from extermities of major axis and P from the centre of the ellipse on the same tangent, then (P_(1)P_(2)-P^(2))/(P_(3)P_(4)-P^(2)) equals (where e is the eccentricity of the ellipse)

Unplarised light is passed through a polaroid P_(1) . When this polarised beam passes through another polaroid P_(2) and if the pass axis of P_(2) makes angle theta with the pass axis of P_(1) , then write the expression for the polarised beam passing through P_(2) . Draw a plot showing the variation of intensity when theta varies from 0 to 2pi .

Two players P_(1)and P_(2) are playing the final of a chess championship, which consists of a series of matches. Probability of P_(1) winning a match is 2/3 and that of P_(2) is 1/3. Thus winner will be the one who is ahead by 2 games as compared to the other player and wins at least 6 games. Now, if the player P_(2) wins the first four matches, find the probability of P_(1) wining the championship.

(i) Plotting V vs T for a given mass of an ideal gas at two different fixed pressures P_(1) and P_(2) gives two straight lines, one of which corresponds to P_(1) and the other corresponds to P_(2) . If P_(1) is greater than P_(2) , then which one of thes straight lines will make a larger angle with the T-axis? (ii) Plotting P vs T for a given mass of an ideal gas at two different fixed volumes V_(1) and V_(2) gives two straight lines, one of which corresponds to V_(1) and the other corresponds to V_(2) . if V_(1) is greater than V_(2) , then which one of these straight lines will make a larger angle with the T-axis?