Using the lens maker's formula, R = 2f(n-1) = 2*10*(1.5-1) = 20 cm.

Using the lens maker's formula, f = R/(n-1), we find f = 20/(1.5-1) = 40 cm.

For total internal reflection to occur in a fiber optic cable, the core must have a higher refractive index than the cladding.

Critical angle θc = sin⁻¹(n2/n1) = sin⁻¹(1.5/1.6) ≈ 38.7°.

Critical angle θc = sin⁻¹(n2/n1) = sin⁻¹(1.4/1.5) ≈ 42.0°.

For total internal reflection, the core must have a higher refractive index than the cladding, so it must be greater than 1.45.

The cladding has a lower refractive index than the core, ensuring that light is kept within the core through total internal reflection.

The cladding has a lower refractive index than the core, ensuring that light remains within the core by total internal reflection.

Using the lens formula, we find f = 1/(1/v + 1/u) = 1/(1/30 - 1/10) = 5 cm.

Using the lens formula, 1/f = 1/v - 1/u. Here, v = 40 cm, u = -20 cm. Solving gives f = 10 cm.

Using the magnification formula, m = h'/h = -v/u. Here, h' = 5 cm, v = 40 cm, u = -20 cm. Thus, h = (h' * u) / v = (5 * -20) / 40 = 2.5 cm.

Using the lens formula 1/f = 1/v - 1/u, where u = -60 cm and v = 20 cm, we find f = 30 cm.

Using the lens formula 1/f = 1/v - 1/u, we have 1/f = 1/15 - 1/60. Solving gives f = 10 cm.

Using magnification m = -v/u = 3, we find v = -60 cm and then use the lens formula to find f = 15 cm.

Using the lens formula and magnification, we find the focal length to be 15 cm.

A virtual image is formed by a concave lens when the object is placed within its focal length.

Using the lens formula, 1/f = 1/v - 1/u, we find f = 4 cm.

Using the lens formula 1/f = 1/v - 1/u, where v = -20 cm and u = -10 cm, we find f = 5 cm.

A virtual image formed by a lens indicates that it is a concave lens.

A positive focal length indicates that the lens is a convex lens, which converges light rays.

A negative focal length indicates that the lens is a concave lens.

Using the lens formula, we find the image distance to be 40 cm.

Since the object distance is greater than the focal length, a real and inverted image is formed.

Power (P) is given by P = 1/f (in meters). Thus, f = 1/P = 1/2 = 0.5 m.

Power (P) = 1/f (in meters), so f = 1/2.0 = 0.5 m = 50 cm.

Power (P) = 1/f (in meters). Therefore, f = 1/2.5 = 0.4 m = 40 cm.

Power (P) = 1/f, so f = 1/P = 1/2.5 = 0.4 m.

Power (P) = 1/f (in meters). Therefore, f = 1/P = 1/5 = 0.2 m = 20 cm.

A negative power indicates a concave lens.

A negative power indicates that the lens is a concave lens.