Question

Please solve this numericals

⚠️❌ N SPAMING ❌❗⚠️

NUMERICAL PROBLEMS

1. A beam of light passes from air to a medium X. If the angle of incidence is 45° and angle of
refraction is 30°, calculate the refractive index of X.


2. The refractive index of glass with respect to air is 1.5. What will be the refractive index of air with respect to glass?​

Answer 1

Answer:

1. A beam of light passes from air to a medium X. If the angle of incidence is 45° and angle of refraction is 30°, calculate the refractive index of X.

Ans :- If angle of incidence is 45 degrees and angle of refraction is 30 degrees calculate the refractive index of substance x. Given: sin30 degrees =1/2 and sin45° = 1/√2.

2. The refractive index of glass with respect to air is 1.5. What will be the refractive index of air with respect to glass?

Ans :- 0.67

(refractive index of glass with respect to air)×(refractive index of air with respect to glass)=1 . this is normally thought in your class 9or 10. so refractive index of air with respect to glass=1/1.5 =0.67.

Answer 2

$\large\underline\blue{\bold{Given \: Question \: 1 :- }}$

• A beam of light passes from air to a medium X. If the angle of incidence is 45° and angle of refraction is 30°, calculate the refractive index of X.

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$\bf \:\large \red{AηsωeR : 1.} ✍$

$\large \green{\bf \:Given :- }$

• A beam of light passes from air to a medium X.
• The angle of incidence is 45°
• The angle of refraction is 30°.

$\large \blue{\bf \:To  \: Find :- }$

• The refractive index of X.

$\large\underline\blue{\bold{Formula \: used:- }}$

$\bf \:Refractive \: index = \dfrac{sin \: i}{sin \: r}$

☆where,

• i = angle of incidence
• r = angle of refraction

$\large\underline\purple{\bold{Solution :- }}$

$\begin{gathered}\begin{gathered}\bf Given \: that = \begin{cases} &\sf{angle \: of \: incidence, \: i = 45°} \\ &\sf{angle \: of \: refraction, \: r = 30°} \end{cases}\end{gathered}\end{gathered}$

☆We know,

$\bf \:\large \red{Refractive \: index = \dfrac{sin \: i}{sin \: r} }$

$\large \blue{\bf \:  ⟼ Refractive \: index = \dfrac{sin \: 45}{sin \: 30} }$

$\large \blue{⟼\bf \:Refractive \: index = \dfrac{\dfrac{1}{ \sqrt{2} } }{\dfrac{1}{2} } }$

$\bf \:\large \blue{⟼ Refractive \: index = \dfrac{1}{ \sqrt{2} } \times \dfrac{2}{1} }$

$\bf \:\large \purple{⟼ Refractive \: index = \sqrt{2} = 1.414 }$

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$\large\underline\blue{\bold{Given \: Question \: 2:- }}$

• The refractive index of glass with respect to air is 1.5. What will be the refractive index of air with respect to glass?

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$\bf \:\large \red{AηsωeR : 2.} ✍$

$\large\underline\purple{\bold{Given \: :- }}$

• The refractive index of glass with respect to air is 1.5.

$\large \green{\bf \:To  \: Find :- }$

• The refractive index of air with respect to glass.

$\large\underline\purple{\bold{Solution :- }}$

▪︎Let refractive index of glass with respect to air is x.

▪︎Let the refractive index of air with respect to glass is y.

$\begin{gathered}\bf\red{According \: to \: statement}\end{gathered}$

$\bf \:⟼ \: x \: = 1.5$

☆We know that,

$\large \blue{\bf \:  ⟼ x \times y = 1}$

$\large \green{\bf \:  ⟼ y = \dfrac{1}{x} }$

$\large \blue{\bf \:  ⟼ y = \dfrac{1}{1.5} = \dfrac{10}{15} = \dfrac{2}{3} = 0.667}$

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