(a) If a person wears lens of power - 6D for distant vision and for correcting his near vision he needs a…
(a) If a person wears lens of power - 6D for distant vision and for correcting his near vision he needs a lens of +2D. Determine the focal length of the lenses in both the case.
(b) Give reason for the following natural phenomenon:
(i) Stars twinkle
(ii) Planets do not twinkle
(iii) Stars appear raised in the sky.
Solution
(a) (i) For distant vision, $P_1 = -6\ \text{D}$
$f_1 = \dfrac{1}{P_1} = \dfrac{1}{-6}\ \text{m} = -\dfrac{100}{6}\ \text{cm} = -16.66\ \text{cm}$
(ii) For near vision, $P_2 = +2\ \text{D}$
$f_2 = \dfrac{1}{P_2} = \dfrac{1}{2}\ \text{m} = +0.5\ \text{m} = +50\ \text{cm}$
(b) (i) Due to continuous changes in the densities of the atmospheric layers, the apparent position of a star keeps changing, which makes the light coming from the distant point-sized star appear brighter and dimmer. This shaking appearance gives the impression of twinkling.
(ii) Planets are much closer to us and act as a collection of a large number of point-sized sources of light. The changes in the light coming from these many points average out, so planets do not appear to twinkle.
(iii) Due to atmospheric refraction, light from a star bends towards the normal as it enters denser air, so a star appears slightly higher than its actual position in the sky.