Question

Find the refractive index if angle of incidence is 45 and angle of refraction is 60 degree

Answer 1

Answer:

0.81664

Explanation:

The refractive index= sin i/ sin r

= sin 45° / sin 60°

= (1/√2)/( √3/2)

= 2/(√2*√3)

=2/ (1.414* 1.732)

=2/2.449048

= 0.81664

Answer 2

$\checkmark$ Given:

• Angle of Incidence = 45°
• Angle of Refraction = 60°

$\checkmark$ To Find:

Refractive Index

$\checkmark$ Solution:

We know that,

Snell's Law:

$\red{\bigstar \ \boxed{\rm n=\dfrac{sin \ i}{sin \ r}}}$

Here,

• n = Refractive Index
• i = Angle of Incidence
• r = Angle of Refraction

Given that,

• Angle of Incidence = 45°
• Angle of Refraction = 60°

Hence,

• i = 45°
• r = 60°

According to the Question,

We are asked to find the Refractive index

So, we should find "n"

Therefore,

By Substituting the above values

We get,

$\blue{\rm \implies n=\dfrac{sin \ 45}{sin \ 60}}$

We know that,

$\orange{\rm \longrightarrow sin \ 45^{\circ}=\dfrac{1}{\sqrt{2}}}$

$\orange{\rm \longrightarrow sin \ 60^{\circ}=\dfrac{\sqrt{3}}{2}}$

Hence,

$\green{\rm \implies n=\dfrac{\dfrac{1}{\sqrt{2} }}{\dfrac{\sqrt{3} }{2}}}$

$\red{\rm \implies n=\dfrac{1}{\sqrt{2} } \times \dfrac{2}{\sqrt{3} }}$

We know that,

2 can also be written as

$\orange{\longrightarrow \rm 2=\sqrt{2} \times \sqrt{2} }$

Hence,

$\red{\rm \implies n=\dfrac{1}{\sqrt{2} } \times \dfrac{\sqrt{2} \times \sqrt{2} }{\sqrt{3} }}$

By Cancelling common terms i.e., ($\red{\rm \sqrt{2}}$)

We get,

$\pink{\rm \implies n=\dfrac{\sqrt{2} }{\sqrt{3}}}$

We know that,

• $\orange{\rm \sqrt{2}=1.414}$
• $\orange{\rm \sqrt{3} =1.732}$

By Substituting the above values

We get,

$\blue{\rm \implies n=\dfrac{1.414}{1.732}}$

$\rm \implies n=0.8163$

$\pink{\rm \implies n \approx 0.81}$

Therefore,

$\checkmark$ Refractive Index = 0.81