Surface of certain metal is first illuminated with light of wavelength $$\lambda $$₁ = 350 nm and then, by light of wavelength $$\lambda $$₂ = 540 nm. It is found that the maximum speed of the photo electrons in the two cases differ by a factor of 2. The work function of the metal (in eV) is close to :

(Energy of photon n = $${{1240} \over {\lambda (in\,mm)}}$$eV)

For a uniformly charged ring of radius R, the electric field on its axis has the largest magnitude at a distance h from its center. Then value of h is :

A heavy ball of mass M is suspendeed from the ceiling of a car by a light string of mass m (m < < M). When the car is at rest, the speed of transverse waves in the string is 60 ms^$$-$$1. When the car has acceleration a, the wave-speed increases to 60.5 ms^$$-$$1. The value of a, in terms of gravitational acceleration g, is closest to :

Consider a tank made of glass(refractive index 1.5) with a thick bottom. It is filled with a liquid of refractive index $$\mu $$. A student finds that, irrespective of what the incident angle i (see figure) is for a beam of light entering the liquid, the light reflected from the liquid glass interface is never completely polarized. For this to happen, the minimum value of $$\mu $$ is :