In a Young's double slit experiment performed in air, the fringe width observed on the screen is 0.50 mm . When the entire apparatus is immersed in an unknown transparent liquid, the new fringe width is measured to be 0.40 mm . If the speed of light in vacuum is 3 10^8 m/s , the speed of light in this liquid is :

Step-by-step solution

The fringe width in air is given by _ air = D d . When the apparatus is immersed in a liquid of refractive index , the wavelength of light becomes ' = . The new fringe width in the liquid is _ liquid = ' D d = D d = _ air . From this, the refractive index of the liquid is: = _ air _ liquid = 0.50 0.40 = 1.25 The speed of light in the liquid is: v = c = 3 10^8 1.25 = 2.40 10^8 m/s . Answer: 2.40 10^8 m/s