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The chapter Ray Optics deals with the study of Laws of Reflection, Deviation, Concept of Mirrors, Focal Principals, etc. The chapter holds the weightage of around 4% in NEET. Ray Optics is also known as Geometrical Optics.

In **NEET 2021** examination, you can expect 2-3 questions from this chapter. The questions could be direct sales this chapter has various definitions and formulas from where direct questions of 4-8 marks could be asked. **Also Check NEET Physics Exam Pattern**

Read the article to know more details about various sub topics of Ray Optics.

## Quick Study Notes of Important Topics

### What is a Ray?

As light travels through a homogenous medium along the straight-line path, it is called a Ray.

### What is Reflection of Light?

Reflection can be termed as a phenomenon where a ray of light, on hitting a boundary, is reverted back to the same medium it originated from. The boundary can be anything ranging from a rigid surface or an interface between two media.

## Law of Reflection

Before we delve into the discussing Law of Reflection, it is of utmost importance to understand the following angles:

### Angle of Incidence

It is an angle that the incidence ray forms with normal at the point of incidence as illustrated in the diagram below:

### Angle of Reflection

- An angle formed by the reflected ray at the point of incidence is known as the Angle of Reflection as illustrated in the diagram below:
- A reflected ray is located at the plane of incidence and forms an angle of reflection equal to that of the angle of incidence. It can be depicted as follows :

∠i = ∠r

- The plane on which the incidence ray, the reflected ray and normal to the reflecting surface at the point of incidence lie, is perpendicular to the reflecting surface as illustrated in the figure below:

### Sample Question

Q : What will be the angle of reflection for a ray of light incident towards a plane mirror at an angle of 30° with the mirror surface ?

- 55°
- 85°
- 60°
- None of the above.

Ans : 60°

## What is Deviation and its concepts?

The path of a ray of light changes as it gets reflected. The angle formed between its direction after reflection and the direction before reflection is known as Deviation as seen in the figure below.

### Reflection by a Plane Surface

If we rotate a reflecting surface by an angle 0 (anticlockwise) and keep the incidence ray fixed then there is reflect ray rotation by 20 along the same sense, which is, anticlockwise.

### Reflection from Plane Mirror

The image of an object can be seen behind the mirror after the object has been kept in front of the plane mirror. The distance of the object from the mirror equals the distance of the image from the mirror.

#### Spherical Mirrors

Parts of a Sphere are called spherical mirrors. The other surface of in them acts as a reflecting surface when one of the surfaces is painted silver.

#### Concave Mirror

It is a kind of spherical mirror that appears bulging at the edges and depressed at the center when it is looked from the reflecting side.

#### Convex Mirror

When this type of spherical mirror is looked from the reflecting side, it appears to be bulging at the center and depressed at the edges.

### Sample Question

Q : A concave mirror gives real, inverted and same size image if the object is placed..

- At F
- At infinity
- At C
- Beyond C

Ans (c) At c

What is Radius of Curvature?

## What is Radius of Curvature, Principal Focus and Other Concepts?

- Radius of Curvature: It is the radius of the sphere with the mirror forming its part.
- Principal Focus: Principal Focus is the point located on the Principal Axis. It is at the Principal Focus where a beam coming along the principal axis meets after getting reflected from the mirror.
- Focal Plane: Perpendicular to the principal axis, Focal Plane is a vertical plane traversing through the principal focus.
- Focal Length: The distance of the principal focus of Focal Length from its pole is known as Focal Length.

### Relation – Focal Length and Radius of Curvature

#### f = R/2

It denotes that the focal length of a spherical mirror amounts to half of its radius of curvature.

### Mirror Formula

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

### Sample Question

Q : Image formed by plane mirror is

- Real and erect
- Real and inverted
- Virtual and erect
- Virtual and inverted

Ans : (c) Virtual and erect

### Calculating relative positions, size and nature of image as an one brings an object from Infinity to the pole of a concave mirror :

(a) If the object is at infinity, u = ∞

v = -f , m = 0

Image obtained at the focus of a focal plane and small in dimensions.

(b) If object lies beyond centre of curvature,

2f > v >f

(c) If object is at centre of curvature,

v = -2f , m =1

Thus, a real and inverted image of same size as that of object gets formed at centre of curvature

(d) Object is in between a distance f and 2f , i.e., in between focus and centre of curvature (f < u < 2f):-

v < ∞ and m = (v/u) >1

Thus, a real, inverted and magnified image is made in between centre of curvature and infinity.

(e) Object is kept at focus (u = -f):-

v = -∞

Rendering of rays after reflection into a parallel beam in infinity

(f) Object is kept within focus (u < -f):-

v is positive.

In this way, a virtual, erect and magnified image is made on the other side of mirror

### Sample Question

Q : Focal length of plane mirror is

- At infinity
- Zero
- Negative
- None of these

Ans : (a) at infinity

**Must Read:**

## What is Refraction and its Concepts?

### Refraction

In the phenomenon of Refraction, a ray of light passing from one medium to the other changes its velocity.

- Incident Ray

It is the ray that approaches the interface.

- Refracted Ray

Ray that goes into another medium

- Laws of Refraction

(a)Snell’s Law : The sine of the angle of incidence shares a constant ratio with the sine of the angle of refraction.

sin i/sin r = constant

(b)The plane in which the Incident Ray, the Refracted Ray and the normal to the interface lie, is perpendicular to the interface separating the two media.

- Refractive Index
- The ratio between the sine of the angle of incidence to the sine of angle of refraction is defined as the Refractive Index of a medium.sin i/sin r = constant = 1µ2
- The ratio between velocity of light in medium 1 to the velocity of light in medium 2 is defined as the Refractive index of medium 2 with respect 1.
- 1µ2 = v1/v2
- µ = c/v
- The ration between absolute refractive index of second medium to the absolute refractive index of first medium is defined as the Refractive index of a second medium with respect to first.
- 1µ2 = µ2/µ1?

- Refraction at a single spherical surface when light travelling from medium of refractive index μ1 (rarer) to that of refractive index μ2 (denser):-

- Refraction at a convex surface producing real image:-

μ2/v – μ1/u = μ2 - μ1/R

- Refraction at a convex surface producing virtual image:-

μ2/v – μ1/u = μ2 - μ1/R

- Refraction at a concave surface:-

μ2/v – μ1/u = μ2 - μ1/R

- Refraction at a single spherical surface when light travelling from medium of refractive index μ2 (denser) to that of refractive index μ1(rarer) :-

Convex surface producing a real image of a real object:-

μ2/u – μ1/v = μ2 - μ1/R

- Light travelling from air to glass:-

μ/v – 1/u = μ-1/R

- Light travelling from glass to air:-

μ/u – 1/v = μ-1/R

- Principal focal length:-

- Second principal focal length:- Second principal focal length of a surface is the distance of that point from the pole of the surface at which a beam coming parallel to principal axis meets or appears to meet after refraction through the surface.

f2 = μ2R/ [μ2 - μ2]

- First principal length:- First principal focal length of a surface is defined as the distance of that point from the pole of surface from where if a beam diverges or to which a beam converges, the rays after refraction through the surface become parallel to principal axis.

f1 = -μ1R/ [μ2 – μ1]

- Relation between f1 and f2:-

f2/v + f1/u = 1

## Lens and its concepts

A portion of refracting material bound between two spherical surfaces is called a lens.

- Converging lens:-

A lens is said to be converging if the width of the beam decreases after refraction through it.

- Diverging lens:-

A lens is said to be diverge if the width of the beam increases after refraction through it.

- Center of curvature:-

Center of curvature of a surface of a lens is defined as the center of that sphere of which that surface forms a part.

- Radius of curvature:-

Radius of curvature of a surface of a lens is defined as the radius of that sphere of which the surface forms a part.

- Lens formula:-

1/f = 1/v – 1/u

- Linear magnification:-

It is the ratio between the size of the image to the size of the object.

m = I/O

Expression for m in terms of u, v and f :-

- In terms of v and f:- m = [f-v] / f
- In terms of u and f:- m = f / [f+u]

- Position of the image as the object is gradually moved from infinity to the pole of the lens:-
- Object being at infinity:- v = f, Magnification in this case is extremely small and the image is said to be real and inverted.
- Object lying beyond 2f:- 2f > v > -f, m(= v/u) always is less than one.
- Object at 2f:- v = 2f, m = -1
- Object lying between f and 2f:- v >2f, m(= v/u) always is greater than one.
- Object at f:- v = ∞, m(= v/u) is infinite.
- Object lying between f and optical center C:-

At f, u = -f. So, v = ∞

At C, u = 0, So, v = 0

- Refraction through a thin double convex lens when the medium on the two sides of the lens is same (Lens maker’s formula):-

1/f = (μ – 1) (1/R1 – 1/R2)

- Refraction through a thin double convex lens when the medium situated on the two sides of the lens is different:-

1/f = [[μ3 – μ1]/μ3R1] + [[μ3 – μ2]/μ3R2]

- Double concave lens:-

- When the medium situated on the two sides of the lens is same:-

1/f = (μ – 1) (1/R1 – 1/R2)

- When the medium situated on the two sides of the lens is different:-

1/f = [[μ3 – μ1]/μ3R1] + [[μ3 – μ2]/μ3R2]

- Combination of two convex lenses in contact:-

F = f1f2 / f1+ f2

- Power of a lens:-

The reciprocal of the focal length of a lens, expressed in meter, is called its power.

P = 1/f

- Refraction through a prism:-

μ = sin [(A+dm)/2] / sin [A/2]

Here, dm is the minimum angle of deviation.

- Refraction through a prism for small angle of incidence:-

d = A (μ-1)

This signifies that the angle of deviation d is independent of the angle of incidence, provided it is small.

### Sample Question

Q : The lens which diverges light from a single point is

- concave lens
- convex lens
- biconvex lens
- all of above

Ans : (a) concave lens

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## Dispersion and its concepts

⦁ Dispersion:- The splitting of light into its constituent colors is called dispersion.

⦁ Cauchy’s formula:- μ = A+(B/λ2)+…

Here A and B are constants and λ is the wavelength of light.

⦁ Refraction through a prism:-

(a) Deviation:- A ray of monochromatic light (light possessing one wave-length only), while passing through a prism suffers a change in its path, the phenomenon is known as deviation.

d = (μ-1) A

Here A is the refractive angle of prism and μ is the refractive index of the material of prism for that particular wave length of light.

(b) Dispersion:- A ray of light (containing more than one wavelengths), while passing through the prism splits up into a number of rays. The phenomenon is called dispersion.

dv = (μv-1) A

dr = (μr-1) A

Here dv is deviation for violet and dr is the deviation for red color. μv and μr be the refractive indices of the material of prism for violet and red colors.

Since, μv > μr, therefore dv is greater than dr.

⦁ Dispersive power (ω):- Dispersive power of a prism is defined as the ratio between angular dispersion to mean deviation produced by the prism.

ω = (dv - dr)/d = (μv – μr)/(μ-1) = dμ/(μ-1)

⦁ Spectrum:- The band of colors lying side-by-side is called spectrum.

(a) Impure spectrum:- Impure spectrum is a spectrum in which the constituent colors overlap each other.

(b) Pure spectrum:- Pure spectrum is a spectrum in which all the constituent colors occupy different and distinct positions.

Sample Question

Q : With a prism (μ=1.5) having a refracting angle of 300, what will be the deviation of a monochromatic ray incident normally in its one surface will be ?

- 180 36’
- 200 30’
- 180
- 190 30’

Ans: (a) 180 36’

### Optical Instruments

⦁ Power of a concave lens (P):-

P = (100/x) dioptre, Here ‘x’ is the distance of 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/fe)]

f0 is the focal length of object, fe is the focal lengthy of eyepeice and L is the length of microscope tube.

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

M = f0/fe

### Sample Question

Q : With an astronomical telescope having magnifying power for normal adjustment being 10 and the length being 110 cm, what would be the magnifying power of the telescope when the image is formed at the least distance of distinct vision for normal eye?

- -12
- -14
- -16
- -18

Ans : -14

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

M = (f0/fe) [(fe+D)/D]

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

M = F/f

### Sample Question

Q : With an objective of focal length 100 cm and magnifying power 50, what will be the difference between the two lenses in normal adjustment in a Galileo telescope ?

- 150 cm
- 100 cm
- 98 cm
- 200 cm

Ans : 98 cm.

## Previous Year Solved Sample Question

Q : What will be the angle of reflection if the angle of incidence is 30°?

- 30°
- 50°
- 15°
- 60°

Ans : 30°

Q : If the Convex lens focus on a real, point sized image then the object is placed

- At focus
- Between F and 2F
- At infinity
- At 2F

Ans : (c) at Infinity

Q :The radius of curvature of a mirror is 20cm the focal length is

- 20cm
- 10cm
- 40cm
- 5cm

Ans : (b) 10 cm

Q : With an object placed 10 cm from a concave mirror and focal length being 5 cm. what would be the image distance ?

- 15 cm
- 5 cm
- 10 cm
- 20 cm

Ans : 10 cm

Q : A lens which converges the incident rays on a single point is

- convex lens
- concave lens
- biconcave lens
- bioconvex lens

Ans : (a) convex lens

Q : When white light is passed through a hollow prism then there is

- no dispersion and no deviation
- Only dispersion
- Only deviation
- Both dispersion and deviation

Answer: (a) no dispersion and no deviation