Chapter 23, Problem 26Q

To determine

(a) To determine:

If the focal length of a glass converging lens in water will be longer

Answer to Problem 26Q

Solution:

The focal length of a glass converging lens in water is longer than that in air.

Explanation of Solution

The parallel rays striking the glass converging lens from air medium, according to Snell’s law the rays are bent towards the normal and again when it leaves the lens and at the second surface the ray is bent away from the normal. After refraction at the lens surfaces, the rays focus at the focal point.

If the lens is placed in water, the refractive index of the lens in water is reduced.

Now, the parallel rays fall on the lens, whose refractive index is less than previous, bent toward normal. The bent is less than that in air.

As, the parallel rays are only bent less, the rays after refraction at the lens surfaces, the rays are not the much bent rays as before and so it travels focus at a point farther. Hence, the focal point is changed to the right which increases the focal length.

To determine

(b) To determine:

That if the focal length of a glass converging lens in water will be shorter.

Answer to Problem 26Q

Solution:

The focal length of a glass converging lens in water will not be shorter than that in water

Explanation of Solution

The parallel rays striking the glass converging lens from air medium, according to Snell’s law the rays are bent toward the normal and again when it leaves the lens and at the second surface the ray is bent away from the normal. After refraction at the lens surfaces, the rays focus at the focal point.

If the lens is placed in water, the refractive index of the lens in water is reduced.

Now, the parallel rays fall on the lens, whose refractive index is less than previous, bent toward normal. The bent is less than that in air.

As, the parallel rays are only bent less, the rays after refraction at the lens surfaces, the rays are not the much bent rays as before and so it travels focus at a point farther. Hence, the focal point is changed to the right which increases the focal length.

To determine

(c) To determine:

That if the focal length of a glass converging lens in water will be the same as in air

Answer to Problem 26Q

Solution:

The focal length of a glass converging lens in water will not be the same as in air.

Explanation of Solution

The parallel rays striking the glass converging lens from air medium, according to Snell’s law the rays are bent towards the normal and again when it leaves the lens and at the second surface the ray is bent away from the normal. After refraction at the lens surfaces, the rays focus at the focal point.

If the lens is placed in water, the refractive index of the lens in water is reduced.

Now, the parallel rays fall on the lens, whose refractive index is less than previous, bent towards normal. The bend is less than that in air.

As, the parallel rays are only bent less, the rays after refraction at the lens surfaces, the rays are not the much bent rays as before and so it travels focus at a point farther. Hence, the focal point is changed to the right which increases the focal length.