A flint glass plate n 166 rests on the bottom of an aquariu

A flint glass plate (n = 1.66) rests on the bottom of an aquarium tank. The plate is 7.00 cm thick (vertical dimension) and covered with water (n = 1.33) to a depth of 11.8 cm. Calculate the apparent thickness of the plate as viewed from above the water. (Assume nearly normal incidence of light rays.)

Solution

For normal incident ,apperent depth = real depth / index of refraction.

                                                    = real depth / n

For plate base:

The image of the plate base due to it\'s own thickness = real thickness / index of refraction of flint glass

                                                                             = 7 cm / 1.66

                                                                             = 4.2168 cm

Viewed through water , the apperent depth of the base of the plate

               = (depth of water + Apperent thickness of plate due to its own) / (index of refeaction fo water)

              = (11.8 cm + 4.2168 cm) / 1.33

              = 12.042 cm

Viewed through water , the apperent depth of the top of the plate

               = (depth of water ) / (index of refeaction fo water)

              = (11.8 cm ) / 1.33

              = 8.872 cm

Therefore apperent thickness of the plate = apperent depth of base of plate - apperent depth of top of the plate

                                                            = 12.042 cm - 8.872 cm

                                                            = 3.17 cm