A monochromatic light wave with wavelength and frequency in air enters another medium. If the angle of incidence and angle of refraction at the interface are and respectively, then the wavelength and frequency of the refracted wave are

STUDY MATERIALS
COURSES
MORE
SUCCESS STORY
ADMISSION
STORE

Back

JEE ADVANCE

CLASS XI - XII
CRASH COURSE

CLASS XI - XII

CRASH COURSE

JEE MAIN

CLASS XI - XII
CRASH COURSE

CLASS XI - XII

CRASH COURSE

NEET

CLASS XI - XII
CRASH COURSE

CLASS XI - XII

CRASH COURSE

BITSAT

CLASS XI - XII

CLASS XI - XII

CBSE BOARD

CLASS IX

CLASS X

CLASS XI

CLASS XII

CLASS VI

CLASS VII

CLASS VIII

UP BOARD

CLASS IX
CLASS X
CLASS XI
CLASS XII

CLASS IX

CLASS X

CLASS XI

CLASS XII

CUET

CRASH COURSE

CRASH COURSE

Courses

CLASSROOM COURSES
ONLINE COURSES

ONLINE COURSES

Q.
A monochromatic light wave with wavelength $λ_{1}$ and frequency $ν_{1}$ in air enters another medium. If the angle of incidence and angle of refraction at the interface are $45 °$ and $30 °$ respectively, then the wavelength $λ_{2}$ and frequency $ν_{2}$ of the refracted wave are [2023]

1 $λ_{2} = \frac{1}{\sqrt{2}} λ_{1}, ν_{2} = ν_{1}$

2 $λ_{2} = λ_{1}, ν_{2} = \frac{1}{\sqrt{2}} ν_{1}$

3 $λ_{2} = \sqrt{2} λ_{1}, ν_{2} = ν_{1}$

4 $λ_{2} = λ_{1}, ν_{2} = \sqrt{2} ν_{1}$

Ans.
(1)

Snell's law $μ_{1} \sin 45 ° = μ_{2} \sin 30 °$

$\frac{μ_{1}}{μ_{2}} = \frac{1}{\sqrt{2}}$

$\Rightarrow \frac{μ_{1}}{μ_{2}} = \frac{λ_{2}}{λ_{1}} = \frac{1}{\sqrt{2}}$

$\Rightarrow λ_{2} = \frac{λ_{1}}{\sqrt{2}}$

Frequency doesn't change on change in medium.

Solution

Q.
A monochromatic light wave with wavelength $λ_{1}$ and frequency $ν_{1}$ in air enters another medium. If the angle of incidence and angle of refraction at the interface are $45 °$ and $30 °$ respectively, then the wavelength $λ_{2}$ and frequency $ν_{2}$ of the refracted wave are [2023]

1 $λ_{2} = \frac{1}{\sqrt{2}} λ_{1}, ν_{2} = ν_{1}$

2 $λ_{2} = λ_{1}, ν_{2} = \frac{1}{\sqrt{2}} ν_{1}$

3 $λ_{2} = \sqrt{2} λ_{1}, ν_{2} = ν_{1}$

4 $λ_{2} = λ_{1}, ν_{2} = \sqrt{2} ν_{1}$

Ans.
(1)

Snell's law $μ_{1} \sin 45 ° = μ_{2} \sin 30 °$

$\frac{μ_{1}}{μ_{2}} = \frac{1}{\sqrt{2}}$

$\Rightarrow \frac{μ_{1}}{μ_{2}} = \frac{λ_{2}}{λ_{1}} = \frac{1}{\sqrt{2}}$

$\Rightarrow λ_{2} = \frac{λ_{1}}{\sqrt{2}}$

Frequency doesn't change on change in medium.

Want Us to Email you About Special Offers & Updates?

Solution

Q. A monochromatic light wave with wavelength λ1 and frequency ν1 in air enters another medium. If the angle of incidence and angle of refraction at the interface are 45° and 30° respectively, then the wavelength λ2 and frequency ν2 of the refracted wave are [2023]

1 λ2=12λ1, ν2=ν1

2 λ2=λ1, ν2=12ν1

3 λ2=2λ1, ν2=ν1

4 λ2=λ1, ν2=2ν1

Ans. (1) Snell's law μ1sin45°=μ2sin30° μ1μ2=12 ⇒ μ1μ2=λ2λ1=12 ⇒ λ2=λ12 Frequency doesn't change on change in medium.

Want Us to Email you About Special Offers & Updates?

Q.
A monochromatic light wave with wavelength $λ_{1}$ and frequency $ν_{1}$ in air enters another medium. If the angle of incidence and angle of refraction at the interface are $45 °$ and $30 °$ respectively, then the wavelength $λ_{2}$ and frequency $ν_{2}$ of the refracted wave are [2023]

1 $λ_{2} = \frac{1}{\sqrt{2}} λ_{1}, ν_{2} = ν_{1}$

2 $λ_{2} = λ_{1}, ν_{2} = \frac{1}{\sqrt{2}} ν_{1}$

3 $λ_{2} = \sqrt{2} λ_{1}, ν_{2} = ν_{1}$

4 $λ_{2} = λ_{1}, ν_{2} = \sqrt{2} ν_{1}$

Ans.
(1)

Snell's law $μ_{1} \sin 45 ° = μ_{2} \sin 30 °$

$\frac{μ_{1}}{μ_{2}} = \frac{1}{\sqrt{2}}$

$\Rightarrow \frac{μ_{1}}{μ_{2}} = \frac{λ_{2}}{λ_{1}} = \frac{1}{\sqrt{2}}$

$\Rightarrow λ_{2} = \frac{λ_{1}}{\sqrt{2}}$

Frequency doesn't change on change in medium.