Ray optics and optical instruments

The basic definition of Optics is to study the properties of light and it’s propagation through different media and its effects.

Ray optics and Optical instruments is a one of important and interesting concept in CBSE Class 12 Physics.

1. Reflection of Light& spherical Mirrors

• Reflection
• Concave Mirror
• Convex Mirror
• Centre of Curvature
• Radius of curvature
• Pole
• Principal axis

2. New Cartesian Sign Convention
3. Mirror equation
4. Refraction of Light & Snell’s Law
5. Lateral Shift
6. Real& Apparent Depth
7. Apparent Position of the Sun

Reflection of Light& spherical Mirrors

When light travels from one medium to another medium, with different refractive index, two phenomenon’s occurs namely, reflection and refraction. Firstly, we revise the basics of light

Light:  It is in the form of energy which  makes objects visible to us. As per Newton, Light consists of a stream of particles is called corpuscles. And The theory of light proposed by Huygens explains the phenomena of interference, diffraction etc. According to Maxwell electronic theory of light, light consists of electric and magnetic fields and they are in mutually perpendicular directions. Heinrich Hertz produced wavelengths of electromagnetic wave and he proved that these electromagnetic waves possessed all properties of light waves.

Light travels in vaccum with velocity is C= 3.0 x 10⁸ m/s.

Laws of Reflection:

1. The incident Ray, Reflected ray normal at the point of incidence lie in the same plane.

The angle which the incident ray makes with the normal and is equal to the angle which the reflected ray makes with normal

 

Secondly, About spherical mirrors, they are Concave mirror and convex mirror

Concave mirror: It is defined as a spherical mirror which when looked from the reflecting side is depressed at the center and bulging at the edges.

 

Convex mirror:-

Convex mirror is a spherical mirror which when looked from the reflecting side bulges at the center and is depressed at the edges.

• Radius of curvature(R):–

The Radius curvature of a mirror is defined as the radius of that sphere of which the mirror forms a part.

• Principle Axis:

The line passing through the center of the sphere and attaching to the mirror in the exact center of the mirror is the principle axis.

• Pole:

Pole is a midpoint of the aperture of the spherical mirror

Principal focus

It is a point, situated on the principal axis, at which a beam coming parallel to principal axis meets or appears to meet after reflection from the mirror.

• Focal plane:-

Focal plane a vertical plane passing through the principal focus and perpendicular to the principal axis.

• Focal length (f):–

Focal length, of a spherical mirror, is the distance of its principal focus from its pole.

• Relation between focal length and radius of curvature:-

f = R/2

it signifies the focal length of a spherical mirror is half of its radius of curvature.

• Mirror formula:-

1/f = 1/v + 1/u = 2/r

• Refraction:–

 Refraction is the phenomenon by virtue of which a ray of light going from one medium to the other undergoes a change in its velocity. The following are basic terms of refraction.

• Incident ray:–The ray which approaches the interface is called incident ray.
• Refracted ray:- Ray which goes into the second medium is called angle of incidence.

Laws of refraction:-

(a) Snell’s law:- The sine of the angle of incidence bears a constant ratio with the sine of the angle of refraction.

sin i/sin r = constant

(b) The incident ray, the refracted ray and the normal to the interface at the point of incidence all lie in one plane and that plane is perpendicular to the interface separating the two media.

• Refractive Index:-

(a) Refractive index of a medium with respect to another is defined as the ratio between sine of the angle of incidence to the sine of the angle of refraction.

sin i/sin r = constant = 1µ2

(b) Refractive index of medium 2 with respect to1 is also defined as the ratio between the velocity of light in medium 1 to the velocity of light in medium 2.

(c) 1µ2 = v1/v2

(d) µ = c/v

(e) Refractive index of a second medium with respect to first is defined as the ratio between an absolute refractive index of the second medium to the absolute refractive index of the first medium.

(f) 1µ2 = µ2/µ1?

Lateral Shift:

The speed of light is different in different transparent media. Therefore, when a ray of light moves from air to glass, because of the optical density, the ray bends towards normal. If the ray emerges from the glass slab due to optical density, the ray moves away from the normal. From the graph Lateral shift defined as The perpendicular distance between the incident ray and emergent ray.

Real and Apparent Depth:

An object placed in a denser medium, when seen from the rarer medium, appears to be at a depth smaller than its actual length in the denser medium. This happens due to refraction of light.

d=t{1-1/n}

 

Apparent Position of the Sun:

The rays from the sun travel through space earth’s atmosphere i.e., rarer to denser medium. The rays bend very slightly towards normal and appear to come from the apparent position of the sun. Hence the sun appears to rise a few minutes before the actual rise and for the same reason, it continues to be seen a few minutes after it’s actually set. Therefore the day becomes longer by about 4 minutes due to refraction effects

Optical Instruments:-

• Power of a concave lens (P):-

P = (100/x) dioptre, Here ‘x’ is the distance from a far point of the defective eye, in ‘cm’.

• Magnifying power or magnification of a simple microscope:-

M = 1+ (D/f),

Here, ‘D’ is the distance of distinct vision and ‘f’ is the focal length.

• Magnifying power or magnification of a compound microscope:-

M = L/f₀[1+(D/f_e)]

f₀ is the focal length of the object, f_e is the focal length of the eyepiece and L is the length of microscope tube.

• Magnifying power or magnification of astronomical telescope (Normal Adjustment):-

M = f₀/f_e

• Magnifying power or magnification of astronomical telescope (When the final image is formed at the distance of distinct vision):-

M = (f₀/f_e) [(f_e+D)/D]

• Magnifying power or magnification of Galileo’s telescope:-

M = F/f