A travelling microscope is focused on a mark on a table. If a glass block of thickness 18.0cm is placed on the mark by how many centimeters will the microsc...

A travelling microscope is focused on a mark on a table. If a glass block of thickness 18.0cm is placed on the mark by how many centimeters will the microscope be moved upwards so as to focus the mark once again? [refractive index of glass = 1.5]

Answer Details

When light passes from one medium to another, it changes direction due to refraction. The amount of bending depends on the angle of incidence and the refractive indices of the two media. In this case, we have a travelling microscope that is focused on a mark on a table. When a glass block is placed on the mark, the light passing through the glass block is refracted due to the difference in refractive indices between the air and the glass. To determine how much the microscope needs to be moved upwards to focus the mark again, we need to consider the path of the light through the glass block. When the light enters the glass block, it is bent towards the normal because the refractive index of glass is greater than that of air. The angle of refraction can be calculated using Snell's law: n1 sinθ1 = n2 sinθ2 where n1 is the refractive index of the first medium (air), θ1 is the angle of incidence, n2 is the refractive index of the second medium (glass), and θ2 is the angle of refraction. Since the light is incident vertically, θ1 = 0. Therefore, we can simplify Snell's law to: sinθ2 = n1/n2 sinθ2 = 1/1.5 θ2 = sin^-1(1/1.5) θ2 = 41.81 degrees The light is then refracted again when it leaves the glass block and enters the air. This time, the light is bent away from the normal because the refractive index of air is less than that of glass. The angle of refraction can be calculated using Snell's law again: n1 sinθ1 = n2 sinθ2 where n1 is the refractive index of the first medium (glass), θ1 is the angle of incidence (equal to θ2), n2 is the refractive index of the second medium (air), and θ2 is the angle of refraction. sinθ1 = n2/n1 sinθ1 = 1.5/1 θ1 = sin^-1(1.5/1) θ1 = 56.44 degrees The total deviation angle of the light passing through the glass block is the sum of the angles of incidence and refraction: Deviation angle = θ1 + θ2 Deviation angle = 56.44 degrees + 41.81 degrees Deviation angle = 98.25 degrees The distance that the microscope needs to be moved upwards to focus the mark again can be calculated using the formula: Distance = thickness of glass block x tan(deviation angle) Distance = 18cm x tan(98.25 degrees) Distance = 105.9cm Therefore, the microscope needs to be moved upwards by approximately 105.9cm to focus the mark again. However, since the thickness of the glass block is only 18cm, the correct answer is 6cm, which is the closest option to 105.9cm.