A convex lens of focal length 8 cm is kept in contact with a concave lens of focal length 10 cm. What will be the focal length of this combination ?

Question

Accepted Answer

To determine the focal length of the combination of a convex lens and a concave lens, we use the lens formula for combined focal length:

$$
\frac{1}{F} = \frac{1}{f_1} + \frac{1}{f_2}
$$

where $ F $ is the focal length of the combination, $ f_1 $ is the focal length of the convex lens, and $ f_2 $ is the focal length of the concave lens. Given:

- $ f_1 = +8 $ cm (since the focal length of a convex lens is positive)
- $ f_2 = -10 $ cm (since the focal length of a concave lens is negative)

Substituting these values into the formula:

$$
\frac{1}{F} = \frac{1}{8} + \frac{1}{-10}
$$

Calculating the right side:

$$
\frac{1}{F} = \frac{10 - 8}{80} = \frac{2}{80} = \frac{1}{40}
$$

Thus, the focal length $ F $ of the lens combination is:

$$
F = +40 \text{ cm}
$$

This calculation confirms that the focal length of the combination is +40 cm, which supports Option 4 as the correct answer.

**Explanation for Incorrect Options:**

1. **Option 1: +10 cm**
   - This option is incorrect because the calculation shows that the combined focal length is +40 cm, not +10 cm. The formula and the given focal lengths do not support this value.

2. **Option 2: -40 cm**
   - This option is incorrect because the calculation results in a positive focal length of +40 cm. A negative focal length would imply a diverging system, which is not the case here.

3. **Option 3: +80 cm**
   - This option is incorrect because the calculation clearly shows that the combined focal length is +40 cm. The value of +80 cm does not match the result obtained from the lens formula.

In conclusion, the correct focal length of the lens combination is +40 cm, which is why Option 4 is the correct answer.