Read the following passage and answer the questions.
Aman sets up a thin convex glass lens of focal length 20 cm on an optical bench. He places a lighted candle on one side of the lens and a white screen on the other side. He moves the candle to several positions. Each time, he slides the screen until a sharp image of the flame appears on it. For some positions of the candle, no image can be caught on the screen at all. He then removes the screen and looks at the candle through the lens. In one trial, he places the lens in a glass tank filled with water. In another trial, he places a thin concave lens in contact with the convex lens and looks for the new image. His teacher asks him to note the image distance and the size of the image each time. She also asks him to write the power of each lens in dioptre.
Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A): When the convex lens is placed in water, its focal length increases.
Reason (R): A lens of longer focal length has a smaller power.
In the light of the above statements, choose the most appropriate answer from the options given below:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → Both (A) and (R) are correct but (R) is NOT the correct explanation of (A).
The focal length of a lens depends on the medium around it. In the lens maker’s formula, \( n_{21} \) is the refractive index of the glass with respect to that medium. The lens bends light only because \( n_{21} \) is more than 1.
Assertion (A) When the convex lens is placed in water, its focal length increases. — True. Water has a refractive index of 1.33, close to 1.5 for glass. So the factor \( (n_{21}-1) \) becomes much smaller in water.
\( \begin{aligned} \text{In air: } n_{21}-1 &= 1.5-1=0.5 \\ \text{In water: } n_{21}-1 &= \frac{1.5}{1.33}-1\approx 0.13 \end{aligned} \)
So \( 1/f \) in water is about one-fourth of its value in air. A glass lens of focal length 20 cm in air has a focal length of about 78 cm in water.
Reason (R) A lens of longer focal length has a smaller power. — True. The power of a lens is \( P=1/f \). So a larger \( f \) gives a smaller \( P \).
Why Reason (R) does not explain Assertion (A)?
R is a result of the longer focal length. Once \( f \) becomes longer in water, the power falls. So R follows from A and does not cause it.
The real cause is the smaller refractive index of glass with respect to water. It is about 1.13, against 1.5 with respect to air. So \( (n_{21}-1) \) and \( 1/f \) become smaller, as in Example 9.7.
NCERT (2026-27):
Example 9.7 – “… For the same glass lens in water, n2 = 1.5, n1 = 1.33. … we find f = + 78.2 cm.”
Power of a lens – “… Thus,”
\( \displaystyle P=\frac{1}{f} \)\( \qquad (9.25) \)