Question

an equi bi-convex lens of focal length 10 cm is cut into two halves making two plano convex lenses. both the plano convex lenses are turned so that their curved surface come in contact. (i) what is the focal length of each plano convex lens?

Answer 1

The focal length of each plano-convex lens is 40 cm.

Step-by-step explanation:

To find the focal length of each plano-convex lens, we can use the lens formula:

1/f = (n - 1) * (1/R1 - 1/R2)

Since the lens is equi bi-convex, both surfaces have the same radius of curvature. Let's assume the radius of curvature of each surface of the lens is R cm. Therefore, the radius of curvature of one surface would be R1 and the other surface would be R2.

Substituting the given values into the lens formula:

1/f = (1.5 - 1)(1/R - 1/R) = 0.5/R

Since the focal length of the original lens is 10 cm (f = 10 cm), we can solve the equation to find the value of R:

R = 2 * f = 2 * 10 = 20 cm

Now we can find the focal length of each plano-convex lens by substituting the value of R into the lens formula:

1/f = 0.5/20 = 0.025 cm-1

f = 1/0.025 = 40 cm

Therefore, the focal length of each plano-convex lens is 40 cm.