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The most Important points of Light—Reflection and Refraction (part-2)
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20. Refraction of light: When a ray of light passes from one transparent medium to another, it bends from its path at the surface of separation. This phenomenon is known as 'refraction of light'.
21. Laws of refraction of light:
(i) The incident ray, the refracted ray and the normal at the point of incidence all lie in the same plane.
(ii) For a given pair of media, the ratio of the sine of the angle of incidence to the sine of the angle of refraction is a constant. This constant is called refractive index (n) of the second medium with respect to the first medium.
Sin i / sin r = n (a constant)
The second law is called snell's law of refraction.
22. Refractive index: The refractive index n of a transparent medium is the ratio of the speed of light in vacuum (c) to the speed of light in that medium (v).
speed of light in vacuum c
n= ———————————— = —
speed of light in medium v
23. Relative refractive index: The relative refractive index of medium 2 with respect to medium 1 is the ratio of speed of light (V1) in medium 1 to the speed of light (V2) in medium 2.
24. Refraction through a rectangular glass slab: For refraction through a glass slab, the emergent ray is parallel to the incident ray but it is laterally displaced from the direction of incident ray.
25. Relation between real depth and apparent depth: Due to Refraction of light, the apparent depth of an object placed in a denser medium is less than the real depth.
26. Definitions in connection with sphereical lenses:
(i) Lens: It is a portion of a transparent medium bounded by two surfaces, at least one of which is a curved surface.
(ii) Concave lens: It is thicker at the centre than at the edges. It converges a parallel beam of light on refraction through it. It has a real focus.
(iii) Concave lens: It is thinner at the centre than at the edges. It diverges a parallel beam of light on refraction through it. It has a virtual focus.
(iv) Centre of curvature: The centre of curvature of the surface of a lens is the centre of the sphere of which it forms a part. Because a lens has two surfaces, so it has two centres of curvature.
(v) Radius of curvature: The radius of curvature of the surface of a lens is the radius of the sphere of which the surface forms a part.
(vi) Principal axis: It is the line passing through the two centres of curvature of the lens.
(vii) Principal focus: A beam of light parallel to the principal axis either converges to a point or appears to diverge from a point on the principal axis after refraction through the lens. This is called ‘Principal focus’. A lens has two principal focii.
(viii) Optical centre: It is a point suited within the lens through which a ray of light passes undeviated.
(ix) Focal length: It is the distance between the principal focus and the optical centre of the lens.
(x) Aperture: It is the diameter of the circular boundary of the lens.
27. New Cartesian sign convention for spherical lenses:
(i) All distances are measured from the optical centre of the lens.
(ii) The distances measured in the direction of incident light are taken positive.
(iii) The distances measured in the opposite direction of incident light are taken negative.
(iv) Heights measured upwards and perpendicular to the principal axis are taken positive.
(v) Heights measured downwards and perpendicular to the principal axis are Taken negative.
For a convex lens, the focal length f is positive and for concave lens f is negative.
28. Lens formula: This formula gives relationship between object distance (u), image distance (v) and focal length (f) of a spherical lens.
1/v - 1/u = 1/f
This formula is applicable to both convex and concave lenses.
29. Linear magnification of a spherical lens (m): It is the ratio of the size of the image formed by the lens (h') to the size of the object (h).
m = h'/h = v/u
In case of convex lens, the magnification m is positive when image is virtual and it is negative when image is real. In case of concave lens, m is always positive as the image formed is always virtual.
For a spherical lens, remember for the linear magnification (m):
Virtual positive, real negative.
30. Power of a lens: It is defined as the reciprocal of the focal length expressed in meters.
P = 1 / f (in meters) = 100 / f (in cm)
S.I. unit of power is 1/m (m-¹), also called dioptre (D). One dioptre is the power of a lens whose focal length is 1 metre. The power of a convex lens is positive and that of a concave lens is negative.
31. Power of lens combination: If a number of lenses are placed in contact with each other, then the net power of the combination is equal to the algebraic sum of their individual powers.
P = P1 + P2 + P3 + .........
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