A biconvex lens of refractive index 1.5 has a focal length of 20 cm20 cm in air. Its focal length when immersed in a liquid of refractive index 1.6 will be:

The focal length of a lens is given by the lensmaker's formula:

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

where: f is the focal length, n is the refractive index of the lens material, R1 and R2 are the radii of curvature of the lens surfaces.

Given that the lens is biconvex, R1 = -R2. Therefore, the formula simplifies to:

1/f = 2(n-1)/R

In air, n = 1.5 and f = 20 cm, so we can solve for R:

1/20 = 2(1.5-1)/R R = 2(0.5)/0.05 = 20 cm

Now, when the lens is immersed in a liquid of refractive index 1.6, the effective refractive index of the lens becomes n' = n/1.6 = 1.5/1.6 = 0.9375.

Substituting n' and R back into the lensmaker's formula gives the new focal length f':

1/f' = 2(0.9375-1)/20 f' = 1/[-0.0625/10] = -160 cm

The negative sign indicates that the lens now acts as a diverging lens. Therefore, the focal length of the lens when immersed in the liquid is -160 cm.