Question

3. The angle of incidence in air for a ray of light is 40°
the ray travels through water of refractive index 4/3
find the angle of refraction.
(Ans. 28.82​

Answer 1

Answer:

ans 28.82

Explanation:

Refractive index refers to the ratio between the speed of an electromagnetic wave in a vacuum and its speed in another medium. It indicates the degree of refraction that would occur in a particular material. Furthermore, the refractive index through a vacuum is 1. One can define the normal as the perpendicular line to the surface of the interface. In such a case, a higher value of refractive index would certainly mean that the bend of the ray is towards the normal.

Refractive Index Formula

The refractive index formula is given as follows:

n =

c

v

where,

n = refractive index of the medium

c = speed of light when in vacuum

v = speed of light when in medium

Refractive Index Formula Derivation

First off all, one must apply the Snell’s law as follows:

For a ray which goes from the air to a medium

Nasin i = nmsin r

Here nm refers to the refractive index of the medium

Na refers to the refractive index of air

i refers to the angle of incidence

r refers to the angle of refraction

Now one must nm the subject of the above equation

Nm =

n

a

s

i

n

i

s

i

n

r

Also, na = 1

Nm =

s

i

n

i

s

i

n

r

Above all, nm =

c

v

=

s

p

e

e

d

o

f

l

i

g

h

t

i

n

t

h

e

v

a

c

u

u

m

s

p

e

e

d

o

f

l

i

g

h

t

i

n

t

h

e

m

e

d

i

u

m

Solved Questions on Resistivity Formula

Q1. A ray of light is transient through a medium to another medium. The angle of the incident comes out to be 30 degrees. Also, the angle of refraction happens to be 50 degrees. Find out the refractive index of the second medium?

Answer: The parameters which are known are:

Angle of incidence (‘i’) = 30 degrees

Angle of refraction (‘r’) = 50 degrees

The refractive index formula is as follows

n =

s

i

n

i

s

i

n

r

n =

s

i

n

30

s

i

n

50

Finally, n =

0.5

0.766

= 0.6527

Q2. Find out the refractive index of the medium such that the speed of light in the medium is 2 × 108 m/s?

Answer: The information we have is,

Speed of light in the medium(‘v’) = 2×108m/s

Speed of light in the vacuum(‘c’) = 3×108m/s

Now, one must apply the formula of refractive index,

So, n =

c

v

n =

3

×

108

2

×

108

n = 1.5