Reflection Through plane surface

aRefraction through Plane SurfaceRefractionRefraction of light is the process of bending of light when it passes from one optical medium to another. For example light bends when it passes from air to water. Rare MediumThe medium in which velocity of light is more is known as optically rare medium.Dense MediumThe medium in which velocity of light is less is known as optically dense medium.Law of refraction 1. The incident ray, the refracted ray and the normal to the interface of two transparent media at the point of incidence, all lie in the same plane.2. When light travels from a rarer medium to denser medium, it bends towards normal and when it travels from denser to rarer, it bends away from normal.3. The ratio of sine of angle of incidence to the sine of angle of refraction is a constant, for the light of a given color and for the given pair of media. This law is also known as Snell’s law of refraction. sin i

sin r = constant This constant is also called the refractive index of the second medium with respect to the first.or, sin i

sin r =𝜇Refractive Index1. Refractive index is defined as the ratio of sine of angle of incidence to the sine of angle of refraction for a given pair of medium. i.e. 𝜇=sin i

sin r 2. Refractive index of a medium is defined as the ratio of velocity of light in air or vacuum to the velocity of light in the medium. i.e. 𝜇=velocity of light in vacuum (c)

velocity of light in the medium (v) or, 𝜇= c

v 3. Refractive index of a medium is defined as the ratio of rea depth to the apparent depth in the medium. i.e. 𝜇=real depth

apparent depth Note:• If the ray of light is passing from air to water we say refractive index of water with respect to air. a𝜇w.• If the ray of light is passing from water to air, we say refractive index of air with respect to water. w𝜇a.• And the relation between these two is a𝜇w=1

w𝜇a• If ray of light is passing from water to glass, we say refractive index of glass with respect to water w𝜇g. This can be determined by the formula w𝜇g=a𝜇g

a𝜇wLateral ShiftWhen a ray of light is incident on a glass slab, the emergent ray coming out of the slab will be parallel to the incident ray. The perpendicular distance between the direction of incident ray and emergent ray is called lateral shift. It is denoted by d.

The figure alongside shows a glass slab MNPS of thickness 't'. A ray of light OA incident at A on the slab surface is refracted as AB inside the slab and finally emerges as BC. N1N2 and N3N4 are the normals at point A and B respectively. BQ perpendicular on direction of incident ray is drawn which is actually the lateral shift. From ΔABQ,we havea sin(i−r)=BQ

AB Or, BQ = AB sin (i– r) ……(1) Again, from ΔABN2, we have, cos r=AN2

AB=t

AB Or, AB=t

cos rSo, equation (1) becomes BQ=t

cos rsin(i-r) or, BQ = tsin(i-r)

cos r or, d = tsin(i-r)

cos rHence when i = 900 d = tsin(90-r)

cos ror, d = tcos r

cos ror d = tThis shows that when light is incident at 900 on the surface of glass slab, lateral shift produced by it is equal to the thickness of the glass slab. Apparent DepthWhen an object is placed is a denser medium and is viewed from rarer medium, it appears to be at a lesser depth (raised up) than its real depth. This is due the refraction of light. Consider an object O at the bottom of water of depth 't'. The ray of light from O ie OA suffers bending away from normal at point A with angle of incident 'i' and angle of refraction 'r' as shown in the figure. We see the image of the object at point 'I' . If M is the point verticaly up at the surface of water, then MO = real depth MI = apparent depth.

From the figure, ∠OAN'=i= angle of incidence in water Also, ∠AOM=∠OAN'=i (alternate angles)Again, ∠NAB=r= angle of refraction in air Also, ∠MIB=∠NAB=r (corresponding angles) and MO=t= depth of waterWhen an object O placed in a denser medium (say water) is viewed from rarer medium (say air), it appears to be raised at point I due to refraction of light which is the virtual image of the object. Thus, OM is called real depth and MI is called apparent depth of the object. According to Snell's law for water air media, we can write, w𝜇a = sin i

sin ror, w𝜇a = MA

OA

MA

IAw𝜇a = MA

OA× IA

MAw𝜇a = IA

OASince, A is very close to M,IA≈IM and OA≈OM. So, we can write,w𝜇a=IM

OMor 1

a𝜇w=IM

OMor 1

a𝜇w=apparent depth

real depthor, a𝜇w = real depth

apparent depth The apparent displacement in the position of the object is called apparent shift (d) which is given by, OI = OM - IM or, d=OM-OM

a𝜇wor d = {1-1

a𝜇w}OMor d = {1-1

a𝜇w}real depthor, d = t{1-1

a𝜇w} This is the expression for apparent shift. Critical Angle and total internal reflection

Critical angleWhen the light is passing from denser medium to rarer medium, the ray of light bend away from the normal so that angle of refraction is greater than the angle of incidence. So, at certain angle of incidence (< 900) in denser medium , the angle of refraction in the rarer medium becomes 900 . The incident angle at denser medium for which angle of refraction at rarer medium is 900 is called critical angle. Total internal reflection: It is defined as phenomenon in which all the light rays reflected into the same denser medium when the light ray incident on the interface of denser and rarer medium at angle of incidence which is greater than the critical angle. Let XYZW be the glass slab which is the denser medium and air is the rarer medium. In fig.(i) PQ is the incident ray incident at the point Q by making angle of incidence i1<C and refracted along QR by making angle of refraction r1. In this case light is refracted.When the ray RQ incident at point Q and refracted along QP by making an angle of refraction r=90∘ and angle of refraction 'i'. g𝜇a = Sin i

Sin ror, 1

a𝜇g =Sin c

Sin 90or, 1

a𝜇g =Sin c

1or sin c = 1

a𝜇gor, c = sin-1(1

a𝜇g)When the ray of light is incident with angle of incidence more than critical angle, it will get reflected, that is it will return to the same medium. So, total internal reflection occurs when:1. ray of light is passing from denser medium to rarer medium2. angle of incidence in denser medium is greater than the critical angle.Example of total internal Reflection1. MirageQ. Why do in summer, roads often appear to be covered with water when seen from a distance? Explain.

In summer, the road gets heated so that the layer of the atmosphere in contact with it also becomes hot whereas the upper layers are relatively cold. Hot air is rarer comparison with cold air hence the rays of light traveling towards the road get refracted away from the normal as they pass from denser to rarer layers of air. At a particular layer of air when the angle of incidence is greater than the critical angle, the phenomenon of total internal reflection occurs and the light gets reflected in upward direction. When this reflected ray reaches the observer's eye, he sees an inverted image of the objects i.e trees. buildings. As they were reflected by the road surface, hence the roads often appear to be covered with water when seen from a distance.2. Sparkling of diamond Total internal reflection is the main cause of the brilliance of the diamond. The refractive index of diamond with respect to air is 2.42. Its critical angle is 24.41°. When light enters a diamond from any face at an angle greater than 24.41° it undergoes total internal reflection. By cutting the diamond suitably, multiple internal reflections can be made to occur. And a bright light comes out from a narrow edge and so seems sparkling. 3. Total reflecting prism

Many optical instruments use right -angled prisms to reflect a beam of light through 900 or 1800 (By total internal reflection) such as cameras, binoculars, periscope and telescope.When a ray of light strikes a face of prism perpendicular, it enters the prism without deviation and strikes the hypotenuse at an angle of 450 . Since the angle of incidence 450 is greater than critical angle of the glass which is 420, the light is totally reflected by the prism through an angle of 900 . Two such prisms are used in periscope. The light is totally reflected by the prism by an angle of 1800. Two such prisms are used in binoculars. Prism is also used to invert images without changing their size.4. Optical Fiber

Optical fiber is the technology associated with data transmission using light pulses travelling along with a long fiber which is usually made of plastic or glass. It works on the principal of total internal reflection. It consists of core of high refractive index , surrounded by cladding with low refractive index. The light beam travels down the core of the cable. When ray of light try to escape out from the core it undergoes total internal reflection and return back. Thus due to multiple total internal reflection light , light remains within the core and travels along the optical fiber even though it is bent. Note: The minimum angle of incident on the cross section of fiber is given by relation sin i = ±𝜇21 -𝜇22Application of optical Fiber1. Optical fiber is used to construct light pine for medical diagnosis (Endoscopy).2. Optical fiber is used in telecommunication.3. They are used in photometry sensor to measure the blood flow in heart.Note: Since optical fiber use the principle of total internal reflection, there is no loss of signal and more over it propagate light not the electric current, hence has least loss of signal and is not affected by electric or magnetic field.Short Questions # Why does a clear pool of water always appear to be shallower than it actually is?

Ans: When the rays of light from the bottom of a clear pool of water comes up. they travel from denser (water) medium to rarer (air) medium and hence behind away from the normal. Thus. if such refracted rays are seen by eyes, the refracted rays which are Actually coming from the point O at the bottom seem to be coming from the point O′ which is above the point O in the water. Due to this, the pool of water appears to be shallower.# Why does the sun look a little oval when it is at the horizon? The effect of the refraction of light while passing through the atmosphere distorts the shape of the sun. The degree of refraction increases as the altitude decreases Hence the lower portion of the sun are raised more than the upper portion. Thus the vertical diameter is shortened while the two extremities of its horizontal diameter are equally raised. As a result the sun appears a little oval.# A ray of light in air strikes a glass surface. Is there a range angles for which total internal reflection takes place. or, Does total internal reflection occur when ray of light travel from rare medium to denser medium?Ans: The condition for the total internal reflection is as follows.(a) The light should pass from denser medium to the rarer medium.(b) The angle of incidence should be greater than the critical angle i.e. i>C.While light moves from denser medium to rare medium, ray of light bends away from normal so that r > i. so at certain condition, r becomes 900 for incident angle less than 900. Which is not possible when ray of light is passing from rare medium to denser medium. Thus as air is rarer medium than glass so there is no range of angle for which total internal reflection takes place.# A stick partially dipped in water seems to be bent. Why?

Ans: When the light passes through one medium 'to another medium then the light bend from normal. As the light passes from rarer medium to denser medium it bends towards normal and as it passes from denser to rarer it bends away from normal. So the stick partially dipped in water seems to bent.