- A beam of light passes from air into a substance X. If the angle of incidence be 72° and the angle of refraction be 40°, calculate the refractive index of substance X. (Given : sin 72° = 0.951 and sin 40° = 0.642)
Ans. The refractive index for light going from air into glass is written as airnglass (or ang where a = air and g = glass)
- Light enters from air into a glass plate having refractive index 1.50. What is the speed of light in glass ? (The speed of light in vacuum is 3×108 m s–1).Ans. The speed of light in glass is 2 × 108 m s–1 (or 2 × 108 m/s)
- The refractive index depends on the nature of the material of the medium and on the wavelength (or colour) of the light used.
- Higher the refractive index of a substance, more it will change the direction of a beam of light passing through it
3. If the refractive index of water for light going from air to water be 1.33, what will be the refractive index for light going from water to air ?
REFRACTION OF LIGHT BY SPHERICAL LENSES
- The working of a lens is based on the refraction of light rays when they pass through it.
- A lens is a piece of transparent glass bound by two spherical surfaces.
- There are two types of lenses : Convex lens and Concave lens
- A convex lens is thick at the centre but thinner at the edges.
- A concave lens is thin in the middle but thicker at the edges
Convergent action of convex lens
- When a convex lens is held facing the sun and the screen is placed at the other side of the lens, by adjusting the distance between the screen and the lens, a sharp and bright spot is obtained on the screen.
- Thus a convex lens is a converging lens.
- When smoke is produced around the concave lens, held in sunlight, the emergent rays are seen to move away from each other.
- Hence a concave lens is a diverging lens.
Each surface of a lens is a part of a sphere.
1 . Centre of curvature of lens (C)
It is centres of the spheres of which the surfaces of a lens form a part.
2. Radii of curvature (R)
It is the radius of the spheres from which the spherical surface was obtained.Since a lens generally has two curved surfaces, it has two radii of curvature.
3. Principal axis
It is a straight line joining the centre of curvatures of the two spherical surfaces of the lens.
- The principal focus of a convex lens is a point on its principal axis to which light rays parallel to the principal axis converge after passing through the lens
- A lens has two foci.
- The two foci of a lens are at equal distances from the optical centre, one on either side of the lens the principal focus of a concave lens is a point on its principal axis from which light rays, originally parallel to the axis, appear to diverge after passing through the concave lens.
- A concave lens has a virtual focus.
Nature of Image formed by Convex Lens
Nature of Image formed by Concave Lens
A formula which gives the relationship between image distance (v), object distance (u), and focal length (f ) of a lens is known as the lens formula.
- A convex lens of focal length 10 cm is placed at a distance of 12 cm from a wall. How far from the lens should an object be placed so as to form its real image on the wall ?
- If an object of 7 cm height is placed at a distance of 12 cm from a convex lens of focal length 8 cm, find the position, nature and height of the image
- An object is placed at a distance of 50 cm from a concave lens of focal length 20 cm. Find the nature and position of the image
- An object placed 50 cm from a lens produces a virtual image at a distance of 10 cm in front of the lens. Draw a diagram to show the formation of image. Calculate focal length of the lens and magnification produced.
POWER OF A LENS
- The power of a lens is a measure of the degree of convergence or divergence of light rays falling on it.
- The power of a lens is defined as the reciprocal of its focal length in metres
- The unit of the power of a lens is dioptre, which is denoted by the letter D
Problem : A convex lens is of focal length 10 cm. What is its power ?
Combination of Lens
- If a number of thin lenses having powers p1, p2, p3, ……etc., are placed in close contact with one another, then their resultant power P is given by :
- P = p1 + p2 + p3 + ………….
Sample Problem: Two thin lenses of power, + 3.5 D and, – 2.5 D are placed in contact. Find the power and focal length of the lens combination