Laws of refraction
1. Sin i / Sin r = refractive index of the medium.
2. Light rays bend when they are incident on a boundary between two media.
3. The incident ray, refracted ray, and the normal to the boundary at the point of incidence, are all in one plane.
Refractive index = 1.5 = speed of light in vacuum / speed of light in glass
=> speed of light in glass = 3 * 10^8 /1.5 = 2 * 10^8 m/sec
concave lens. - forms virtual small erect images
h = 5 cm u = ? v = -15 cm f = - 20 cm
1/v - 1/u = 1/f => 1/u = 1/v - 1/f = -1/15 +1/20 = -1/60
u = -60 cm
m = h'/h = v/u = -15/-60 = 1/4
h' = 5/4 cm
SI unit of Power of lens = a Dioptre = D
SI unit of focal length = meter.
Power = 1 / focal length
Relative refractive index of medium 2 wrt medium 1 = μ₂₁
μ₂₁ = μ₂ / μ₁ = 1.50 / 1.44 = 1.0417
magnification for lenses (magnification for mirrors is defined differently)
m = h'/h = v/u
A virtual image is always erect and in the same direction as the object. Hence h and h' have the same sign. Also, the image and the object are on the same side. Hence the signs of u and v are same.
A real image is inverted on the other side of lens. Hence, h and h' are in opposite directions. Also, u and v are on opposite sides of lens. Hence m is negative.
u = ? f = -10 cm for concave mirror, m = -v/u = -h/h
v = -2 u
1/f = 1/v + 1/u => -1/10 = -1/2u +1/u = 1/2u
u = -5 cm
u = -20 cm v = -(20 + 40) = -60 cm
d) 1/f = -1/20 - 1/60 = -1/15 => f = -15 cm
a) mirror is concave mirror as the focal length is negative. Convex mirror always forms images on the other side (behind) of mirror. ie., v is always positive.
b) m = -(-60)/(-20) = -3 = h'/h image is inverted as h' = -3 h
concave mirror forms erect images when object is within focal length. otherwise, inverted images are formed.
c) see diagram enclosed.