Laws of reflection, spherical mirrors, refraction, Snell's law, lenses, and sign convention
Law 1: The angle of incidence (ā i) equals the angle of reflection (ā r).
Law 2: The incident ray, reflected ray, and the normal at the point of incidence all lie in the same plane.
Concave mirror: Reflecting surface is on the inner (hollow) side. Converging mirror.
Convex mirror: Reflecting surface is on the outer (bulging) side. Diverging mirror.
Centre of curvature (C): Centre of the sphere of which mirror is a part.
Principal focus (F): Point where parallel rays converge after reflection (concave) or appear to diverge from (convex).
Focal length (f): Distance from mirror to focus. f = R/2 (where R = radius of curvature)
Principal axis: Line joining the pole to the centre of curvature.
| Object Position | Image Position | Nature of Image |
|---|---|---|
| At infinity | At F | Real, inverted, highly diminished (point) |
| Beyond C | Between F and C | Real, inverted, diminished |
| At C | At C | Real, inverted, same size |
| Between C and F | Beyond C | Real, inverted, magnified |
| At F | At infinity | Real, inverted, highly magnified |
| Between F and pole | Behind mirror | Virtual, erect, magnified |
Always forms a virtual, erect, and diminished image behind the mirror, regardless of object position.
Used as: Rear-view mirrors in vehicles (gives wider field of view), security mirrors in shops.
ā¢ All distances measured from pole (P) along principal axis
ā¢ Distances in direction of incident light (+ve direction = left to right)
ā¢ Object is always on left ā object distance (u) is always negative
ā¢ Real image: v is negative (same side as object) | Virtual image: v is positive (behind mirror)
Mirror Formula: 1/v + 1/u = 1/f
Magnification: m = āv/u = h'/h
m > 0: virtual, erect image | m < 0: real, inverted image
|m| > 1: magnified | |m| < 1: diminished | |m| = 1: same size
Q: An object is placed 10 cm in front of a concave mirror with focal length 15 cm. Find image position.
u = ā10 cm (object on left), f = ā15 cm (concave mirror)
1/v = 1/f ā 1/u = 1/(ā15) ā 1/(ā10) = ā1/15 + 1/10
= (ā2 + 3)/30 = 1/30 ā v = +30 cm
Image is 30 cm behind mirror ā virtual, erect, magnified
m = āv/u = ā(30)/(ā10) = +3 (magnified 3Ć, erect)
Refraction is the bending of light when it passes from one medium to another (different optical densities).
Cause: Change in speed of light in different media
Law 1: The incident ray, refracted ray, and normal at the point of incidence are all in the same plane.
Law 2 (Snell's Law): nā sin i = nā sin r
Or: sin i / sin r = nā/nā = constant (for given pair of media)
n = speed of light in vacuum (c) / speed of light in medium (v)
n = c/v (n is always ā„ 1)
Higher n = optically denser = light bends more toward normal
n for water ā 1.33 | n for glass ā 1.5 | n for diamond = 2.42
Convex lens (converging): Thicker at centre, converges light. f is positive.
Concave lens (diverging): Thinner at centre, diverges light. f is negative.
| Object Position | Image Position | Nature |
|---|---|---|
| At infinity | At Fā | Real, inverted, point-sized |
| Beyond 2Fā | Between Fā and 2Fā | Real, inverted, diminished |
| At 2Fā | At 2Fā | Real, inverted, same size |
| Between Fā and 2Fā | Beyond 2Fā | Real, inverted, magnified |
| At Fā | At infinity | Real, inverted, highly magnified |
| Between Fā and lens | Same side as object | Virtual, erect, magnified |
Lens Formula: 1/v ā 1/u = 1/f
Magnification: m = v/u
Power of lens: P = 1/f (in metres)
Unit of power: Dioptre (D) | Convex lens: P positive | Concave: P negative
Combined lenses: P = Pā + Pā + Pā ...
Q: An object is placed 15 cm from a convex lens of focal length 10 cm. Find image position and nature.
u = ā15 cm, f = +10 cm
1/v = 1/f + 1/u = 1/10 + 1/(ā15) = 1/10 ā 1/15 = (3ā2)/30 = 1/30
v = +30 cm (positive: real image, opposite side)
m = v/u = 30/(ā15) = ā2 (inverted, magnified 2Ć)
Image: Real, inverted, magnified, 30 cm on other side of lens
1/v + 1/u = 1/f
f = R/2
m = āv/u
nā sin i = nā sin r
n = c/v
1/v ā 1/u = 1/f
m = v/u
P = 1/f (D)