CBSE Class 10 Physics Human Eye and the Colourful World Notes Set 09

The Human Eye

Light enters the eye through the transparent cornea, which does most of the refraction. The iris controls the size of the pupil and so the amount of light entering. The crystalline lens fine-tunes the focus and forms a real, inverted image on the retina, where light-sensitive cells send signals through the optic nerve to the brain, which interprets the image as erect.
The lens-to-retina distance is fixed, so the eye focuses on objects at different distances by changing the focal length of the lens. The ciliary muscles relax to make the lens thin (long focal length) for distant objects, and contract to make it thick (short focal length) for near objects. This power of adjustment is called accommodation.
Far point of a normal eye: infinity. Near point (least distance of distinct vision): about 25 cm. In a dim room the pupil takes a short time to dilate, so we cannot see well for a while after leaving bright light.

Defects of Vision and Their Correction

To correct myopia, the lens must form the image of a distant object at the far point: \( f = -d_{far} \). To correct hypermetropia, the lens must form the image of an object at 25 cm at the near point of the person: use \( \dfrac{1}{f} = \dfrac{1}{v} - \dfrac{1}{u} \) with u = -25 cm and v = -(near point). Power \( P = 1/f \) in dioptres.

Refraction through a Prism

A prism has two inclined refracting faces. A ray bends towards the base on passing through it. The angle of deviation is the angle between the incident ray and the emergent ray. For a prism of angle A: \( i + e = A + \delta \) and \( r_1 + r_2 = A \).
At minimum deviation the ray passes symmetrically, i = e and r = A/2, giving \( \mu = \dfrac{\sin\frac{A + \delta_m}{2}}{\sin\frac{A}{2}} \). For a thin prism, \( \delta = (\mu - 1)A \).

Dispersion of White Light

Dispersion is the splitting of white light into its colours (violet, indigo, blue, green, yellow, orange, red) on passing through a prism, because each colour has a different refractive index and so bends by a different amount. Violet bends the most and red the least. A second prism, inverted relative to the first, recombines the colours into white light, showing that the prism only separates the colours already present. Monochromatic light is only deviated, not dispersed.
A rainbow forms when sunlight is dispersed by raindrops, with internal reflection inside the drop. It is seen when the Sun is behind the observer and rain is in front, with red on the outer edge and violet on the inner edge of the primary bow.

Total Internal Reflection

When light goes from a denser to a rarer medium, it bends away from the normal. At the critical angle C the refracted ray grazes the surface (angle 90 degrees). For an angle of incidence greater than C the light is totally reflected back into the denser medium. Conditions: light must go from denser to rarer, and the angle of incidence must exceed C. \( \mu = \dfrac{1}{\sin C} \).
Examples: sparkling of diamond (C about 24.4 degrees), optical fibres, mirage, and totally reflecting prisms. A right-angled isosceles prism turns a normally incident ray through 90 degrees if the glass has \( \mu \ge \sqrt{2} \).

Atmospheric Refraction and Scattering

The refractive index of air decreases with altitude. Because of atmospheric refraction, stars twinkle, the Sun is seen about 2 minutes before the actual sunrise and about 2 minutes after the actual sunset (making the day about 4 minutes longer), and the Sun's disc looks flattened near the horizon.
Scattering of light by particles smaller than the wavelength follows \( I \propto 1/\lambda^4 \) (Rayleigh scattering), so blue light is scattered most and the sky looks blue. At sunrise and sunset sunlight travels a long path through air, the blue is scattered away and the Sun looks red. To an astronaut the sky is dark since there is no atmosphere. Red light is scattered least, so it is used for danger signals and fog lamps. The Tyndall effect is the scattering of light by colloidal particles that makes a beam visible.

Simple Microscope and Telescope

A simple microscope is a convex lens of short focal length; the object is placed between the optical centre and the focus to get a virtual, erect, magnified image. Magnifying power \( m = 1 + \dfrac{D}{f} \) with D = 25 cm, so a lens of larger power magnifies more. A telescope is used to see large objects at very large distances.