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.
The power of a lens, which Aman writes in dioptre, is defined as
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → the tangent of the angle by which it bends a parallel ray at unit height
Power tells how strongly a lens converges or diverges light. It is measured in dioptre, where \( 1\ \mathrm{D}=1\ \mathrm{m^{-1}} \).
Option (1) the angle through which it turns a ray passing through its optical centre — Incorrect. A ray through the optical centre comes out without any deviation, so this angle is zero for every thin lens.
Option (2) the ratio of the size of the image to the size of the object — Incorrect. This ratio is the magnification. It changes with the position of the object, so it cannot describe the lens itself.
Option (3) the reciprocal of the radius of curvature of its faces, in metre — Incorrect. Power is the reciprocal of the focal length. The focal length depends on both radii and on the refractive index, so \( 1/R \) is not the power.
Option (4) the tangent of the angle by which it bends a parallel ray at unit height — Correct. A ray parallel to the axis at height \( h \) is bent through \( \delta \), with \( \tan\delta=h/f \). For \( h=1 \), \( \tan\delta=1/f \), and this is the power.
NCERT (2026-27):
Power of a lens – “… The power P of a lens is defined as the tangent of the angle by which it converges or diverges a beam of light parallel to the principal axis falling at unit distance from the optical centre …”