Light
Reflection of light
When a beam of light traveling in one homogeneous medium meets a second medium, part of the incident light is turned back in the first medium. This phenomenon is known as reflection of light.
Here PQ is the boundary surface between two media. AO is the incident ray, OB is the reflected ray and NO is the normal. The angle AON which is the angle between the incident ray and normal at the point of incidence is called the angle of incidence.
The angle BON that is the angle between the reflected ray and the normal at the point of incidence is called the angle of reflection.
First law of reflection:
The incident ray, the reflected ray and the normal to the reflecting surface at the point of incidence, all lie in the same plane.
Second Law of reflection:
The angle of incidence is equal to the angle of reflection.
Refraction at a plane surface:
A ray of light travels in a straight line in homogeneous transparent medium. But when light passes from one transparent medium to another transparent medium of different density, it suffers a change of direction at the surface of separation between the two media. This means that a ray of light bends in passing from one transparent medium to another transparent medium of different density. The amount of bending depends on the nature of the two media. The bending of the path of a ray of light while passing from one transparent medium to another transparent medium of different density is known as Refraction of light.
Let PQ represents the surface of separation between two homogeneous transparent media, say air and water. A ray of light AO traveling in air is incident at O obliquely on PQ. Let it be refracted along OB. Then AO represents the incident ray and OB represents the refracted ray. NON/ represents the normal to the surface of separation PQ between the two media at O. So the AON is angle of incidence and the BON/ is the angle of refraction.
It is found that whenever a ray of light passes from a rarer to a denser medium, say from air to water, it bends towards the normal i.e. the angle of incidence is greater than the angle of refraction.
On the other hand, when a ray of light passing from a denser to a rarer medium, it bends away from the normal. So in that case the angle of incidence is smaller than the angle of refraction.
Laws of refraction:
First law: The incident ray, the refracted ray and the normal to the surface of separation of the two media at the point of incidence lie in one plane.
Second law: The ratio of the sine of the angle of incidence to the sine of the angle of the refraction is a constant quantity for any pair of media and for the same color of light. This law was formulated by Snell and known as Snell’s law.
i.e.
Here is called the refractive index of the second medium with respect to the first medium.
Refractive index:
When a ray of light passes from one medium to another medium, then for a particular color and for a particular pair of medium the ratio of the sine of the angle of incidence to the sine of the angle of the refraction is constant which is called refractive index of the second medium with respect to the first medium.
Total internal reflection and critical angle:
When a ray of light passes from a denser to a rarer medium the refracted ray bends away from the normal. This means that the angle of incidence in the denser medium is smaller than the angle of refraction in the rarer medium. So if the angle of incidence in the denser medium is increased gradually, the angle of refraction in the rarer medium also increases gradually according to the law of refraction.
The angle of incidence corresponding to which the angle of refraction just becomes 900 i.e. the refracted ray grazes the surface of separation is known as the critical angle for the pair of media. ‘When light passes from a denser medium to a rarer medium the angle of incidence corresponding to which the angle of refraction just becomes 900 is called critical angle’.
Suppose a ray of light is traveling from a denser to a rarer medium for which the angle of incidence is equal to the critical angle then the angle of refraction is 900 and if the refractive index of the denser medium with respect to the rarer medium is then we can write,
Therefore,
Total internal reflection: It is the phenomenon of reflecting back light into a slightly a denser medium, light being incident from the denser medium at an angle exceeding the critical angle for the pair of media.
When light passes from a denser medium to a rarer medium if the angle of incidence is greater than the critical angle the light ray will reflect back to the denser medium. This phenomenon is known as total internal reflection.
Problem Sheet (Light)
1. If a ray of light incident on the surface of water at an angle of incidence of 600. The refractive index of water is 1.33.
i. Calculate the angle of refraction.
ii. Draw the ray diagram.
2. A ray of light is incident on a rectangular glass block of refractive index 1.5. If the ray strikes the surface PQ at an angle of incidence i of 450 as shown in the figure, calculate:
i the angle of refraction r at the air to glass boundary (PQ)
ii the angle of incidence X in the glass block,
iii the angle of refraction y at the glass–to- air boundary (RS)
3. (a) Label on the diagram the following:
i) reflected ray and refracted ray
ii) angle of incidence
iii) normal
(b) If the angle of incidence is 750 and the angle
of refraction is 400, what is the refractive index
between medium 1 and 2?
(c) If the speed of light in medium 1 is C= , what would be the speed (V) of light in medium 2? [ ]
4. If the refractive index of glass with respect to air is 1.5, calculate the critical angle.
5. Calculate the critical angle of water with respect to air.
6. A man is looking vertically downwards into a tank filled with water, the bottom of which appears to him at a depth of 10 m. Find the actual depth of the tank. Refractive index of water = 1.33.
7. A picture is stuck on the bottom of a glass block 4 cm thick. If the refractive index of glass is 1.6 how much does the picture appear raised to a perpendicular vision?
8. A man uses a lens of focal length 25 cm, what will be the power of the lens and what kind of lens is this?
9. If the power of a lens used by a person who cannot see the near objects is –2D, then calculate the focal length of the lens.
Problems related to lens
1. An object is kept at a distance of 24 cm from the centre of a convex lens having focal length 12 cm. Find the position of the image.
2. An object is placed at a distance of 12cm from the centre of a convex lens having focal length 15 cm. Find the position of the image and draw the ray diagram.
3. What will be the position of the image formed by a convex lens if the object distance is 16cm and the focal length is also 16 cm?
4. If an object of a convex lens of focal length 18 cm is at infinity what will be the image position?
Some Important Definitions:
1. Centre of curvature: A lens is usually bounded by two surfaces which are the parts of two spheres. Each of these two centres of the spheres is known as the centre of curvature of a lens.
2. Principal axis: It is the line passing through the centre of the curvature of the lens.
3. Principal focus: When a beam of parallel rays is incident on a lens in a direction parallel to its principal axis, after refraction through the lens the rays actually converge at a point F on the principal axis or appears to diverge from a point F on the principal axis. This point F is known as the Principal focus of the lens.
4. Focal length: The distance between the principal focus and the optical centre of a lens is called the focal length of the lens.
5. Optical centre: Optical centre of a lens or simply the centre of a lens may be defined as fixed point lying on the principal axis of the lens such that all rays passing through this point within the material of the lens will have their refracted rays parallel to their corresponding incident direction.
6. Power of a lens: When rays parallel to the principal axis pass through the lens the ability of the lens to converge or diverge the rays is called Power of the lens. Power is the reciprocal of the focal length.
Unit of Power of the lens is Dioptre.
