Light Reflection And Refraction

The wavelength of light changes when it passes from one medium to another, and this is governed by the refractive index. The relation between the wavelengths in two different media is given by: where: - is the wavelength of light in the first medium (air in this case), - is the wavelength of light in the second medium, - is the refractive index of the second medium. Given: - , - . Substitute the values into the formula: Thus, the wavelength of light after entering the medium with refractive index 1.5 is .

In Young's double-slit experiment, the fringe width is given by the formula: where: - is the wavelength of the light used, - is the distance between the screen and the slits, - is the distance between the slits. Now, when the wavelength changes, the fringe width changes accordingly. Let the initial wavelength and the initial fringe width . The new wavelength is . We can use the ratio of the fringe widths to find the new fringe width : Substitute the values: Simplifying the right-hand side: Now, solve for : Thus, the new fringe width is .

The power of a lens is related to its focal length ( ) by the equation: where is the power of the lens in diopters (D) and is the focal length in meters. For a lens combination, the total power is the sum of the individual powers: Given that the power of the first lens and the power of the second lens , the total power is: Now, the total focal length can be calculated using the formula: The negative sign indicates that the lens combination behaves as a diverging lens. The focal length of the diverging lens is (since ).
Thus, the combination of the two lenses behaves as a diverging lens with a focal length of .

Let the angle of the prism be and the angle of incidence be . We are given that: At the condition of minimum deviation, the angle of deviation is given by: Now, for minimum deviation in an equilateral prism, the refractive index of the prism is related to the angle of the prism by the following relation: Using Snell's Law at the surface of the prism and knowing that the light undergoes minimum deviation, we also have the relationship between the refractive index and the velocity of light in the glass : Where is the speed of light in vacuum and is the velocity of light in the glass. To find , we need to compute the refractive index . Now using the given information, we can express the refractive index in terms of the given quantities. After performing the necessary calculations, the final value of comes out to be . Thus, the velocity of light in the glass is: Therefore, the velocity of light in the glass is .