Question

Two point white dots are $1mm$ apart on a black paper. They are viewed by eye of pupil diameter $3mm$. Approximately, what is the maximum distance at which these dots can be resolved by the eye? [Take wavelength of light $ = 500nm$]
A) $10m$
B) $5m$
C) $15m$
D) ${\text{None of these}}$

Answer 1

Hint: The ratio of the distance between the dots and the distance from the eye is directly proportional to the ratio of wavelength to diameter of the pupil. Here, the diameter of the pupil is taken as an average diameter under relaxed conditions.

Complete step by step solution:
Wavelength, distance of two consecutive waves between the corresponding points. Two dots or particles in a same phase — dots with similar percentages of their periodic motion. "Coordinating dots" In cross waves (waves with points that oscillate at right angles in the way they progress), wavelength is typically determined in crest to crest and trough to trough waves; the compression to compression or rarefaction to rarefaction was measured at longitudinal waves (waves with vibratory points in the same direction that they advance). The wavelength depends on the medium a wave passes through (e.g., vacuum, air or water). Sound waves, illumination, water waves and normal electronic signals in a conductor are examples of waves. A sound wave is a modification in atmospheric pressure, while the power of the electric and the magnetic field changes in light and other electromagnetic radiation. Water waves are changes in water body height. Atomic locations differ in a crystal grid vibration.
\[\dfrac{y}{D} \geqslant 1.22\dfrac{\lambda} {d}\]
$\lambda $ is the wavelength
$d$ is the diameter of pupil’s eye
$D$ is the maximum distance at which the dots can be resolved by the eye
$y$ is the distance between the two dots.
\[ \Rightarrow D \leqslant \dfrac{{yd}}{{1.22\lambda }} = \dfrac{{{{10}^{ - 3}} \times 3 \times {{10}^{ - 3}}}}{{1.22 \times 5 \times {{10}^{ - 7}}}}\]
 $\therefore$ ${D_ {\max}} = 5m$
Hence, the correct option is B.

Note: Light wavelength varies with colours, i.e. for each colour. The longest wavelength is the red colour and the least is violet. UV emission has a shorter wavelength than violet rays. The ultraviolet emission wavelength is even greater than that of the red light wavelength. Inverse wavelength is commensurate of frequency. The longer the wavelength, the less the frequency. Similarly, higher frequency is the shorter the wavelength.