Question

focal length of a convex lens of refractive index 1.5 is 2 cm. focal length of lens when immersed in a liquid of refractive index of 1.25 will be

Answer 1

The focal length of a convex lens when immersed in a liquid of refractive index 1.25 is 2.825 cm.

Step-by-step explanation:

According to the lens maker's equation, the focal length of a lens can be calculated using the formula:

1/f = (n1 - n2) * (1/R1 - 1/R2)

Where f is the focal length of the lens, n1 and n2 are the refractive indices of the lens and the surrounding medium respectively, and R1 and R2 are the radii of curvature of the two lens surfaces.

For a convex lens with a focal length of 2 cm and a refractive index of 1.5:

1/2 = (1.5 - 1) * (1/R1 - 1/(-R2))

Solving for R1, we get:

R1 = -3 cm

Now, if the lens is immersed in a liquid with a refractive index of 1.25, the formula becomes:

1/f' = (1.5 - 1.25) * (1/R1 - 1/R2)

Substituting the values, we get:

1/f' = (0.25) * (1/(-3) - 1/(-35))

Simplifying, we find:

f' = 2.825 cm

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