Please solve this question.

Please solve this question. Q3. A monochromatic light of wavelength A1 travelling in a medium of refractive index enters a denser medium of refractive index Y2. The wavelength in the second medium is: A. A1 (P2 ¯ PI)/ß2 B. D.

A
 
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Dear friend,

When monochromatic light moves from one medium to another, it's wavelength changes whereas frequency remains same.

--> frequency = same
--> speed (1st medium) = V1
--> speed (2nd medium) = V2

Wavelength in 1'st medium = lambda1
We have to find wavelength in second medium, i.e, lambda2

Refractive index of 1'st medium = U1
------> U1 = C/V1 ----(1)
Refractive index of 2'nd medium = U2
------> U2 = C/V2 ----(2)

Relation between frequency, wavelength and speed of light is :-
---> Speed = frequency * Wavelenth

In rarer medium
---> V1= f1 * lambda1
---> f1 = V1/lmbda1

Similarly :-
---> V2 = f2 * lambda2
---> f2 = V2/lambda2

Since frequency remains same, so
---> f1 = f2

Therefore :-
V1/lambda1 = V2/lambda2 ----(3)

Now,

---> V1 = C/U1
---> V2 = C/U2

Putting the values in equation (3)

--> (C/U1)/lambda1 = (C/U2)/lambda2
--> C/U1 * 1/lambda1 = C/U2 * 1/lambda2

C will be cancelled on both the sides

--> lambda2 = (U1*l ambda1)/U2
--> lambda2 = lambda1(U1/U2)

Hence option A is correct !

Hope it helped !
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Thanks and Regards !
Abhay Pratap Singh......(^^)
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When monochromatic light moves from one medium to another, it's wavelength changes whereas frequency remains same. --> frequency = same --> speed (1st medium) = V1 --> speed (2nd medium) = V2 Wavelength in 1'st medium = lambda1 We have to find wavelength in second medium, i.e, lambda2 Refractive index of 1'st medium = U1 ------> U1 = C/V1 ----(1) Refractive index of 2'nd medium = U2 ------> U2 = C/V2 ----(2) Relation between frequency, wavelength and speed of light is :- ---> Speed = frequency * Wavelenth In rarer medium ---> V1= f1 * lambda1 ---> f1 = V1/lmbda1 Similarly :- ---> V2 = f2 * lambda2 ---> f2 = V2/lambda2 Since frequency remains same, so ---> f1 = f2 Therefore :- V1/lambda1 = V2/lambda2 ----(3) Now, ---> V1 = C/U1 ---> V2 = C/U2 Putting the values in equation (3) --> (C/U1)/lambda1 = (C/U2)/lambda2 --> C/U1 * 1/lambda1 = C/U2 * 1/lambda2 C will be cancelled on both the sides --> lambda2 = (U1*l ambda1)/U2 --> lambda2 = lambda1(U1/U2) Hence option A is correct !
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