Question

Given a double-convex thin lens with refractive index 1.5 , assume that one side of the lens is filled with air (n1​=1) and the other side is filled with water (n2​=1.33). The radii of curvature of the surface of the lens are 10 cm and 15 cm, respectively. Calculate the two focal lengths.

Answer 1

To calculate the focal lengths of the lens for air and water, we use the Lens Maker's Equation, considering the refractive indices and the radii of curvature provided.

Step-by-step explanation:

The student is asking to calculate the focal lengths of a double-convex thin lens which is in contact with air on one side and water on the other side, using the given refractive indices and radii of curvature of the lens surfaces.

To calculate the focal lengths, we use the Lens Maker's Equation, which for a lens in two different media is given by:

1/f = (n - n1)/R1 - (n - n2)/R2,

where n is the refractive index of the lens material, n1 and n2 are the refractive indices of the surrounding media (air and water, respectively), R1 and R2 are the radii of curvature of the lens surfaces, and f is the focal length of the lens.

For the air side (n1 = 1):

1/f_air = (1.5 - 1)/10cm - (1.5 - 1.33)/15cm

and for the water side (n2 = 1.33):

1/f_water = (1.5 - 1.33)/10cm - (1.5 - 1)/15cm

By solving these equations, we can find the focal lengths for the lens when it is in contact with air and with water.