Wave Optics Solved Examples | Physics for JEE Main & Advanced PDF Download

 Page 1


JEE Solved Example on Wave Optics 
JEE Mains 
Q1:  Two coherent monochromatic light beams of intensities I and 4 I are superposed. The 
maximum and minimum possible intensities in the resulting beam are: 
(A) ?? ?? and I 
(B) 51 and 31 
(C) 9 I and I 
(D) 91 and 31 
 Ans: (C) I = ?? 1
+ ?? 2
+ 2 v ?? 1
?? 2
c o s ? ?? ?? max
? c os ? ?? = 1
I = 9 |
I
mi n
? c os ? ?? = - 1
?? mi n
= ?? 
 
Q2 When light is refracted into a denser medium, 
(A) Its wavelength and frequency both increase 
(B) Its wavelength increase but frequency remains unchanged 
(C) Its wavelength decreases but frequency remain unchanged 
(D) It wavelength and frequency both decrease. 
Ans: (C) ?? =
?? ?? 
In denser medium, c decreases but frequency remains the same. 
? ?? also decreases 
 
Q3: In YDSE how many maxima can be obtained on the screen if wavelength of light used is 
?????? ???? and ?? = ?????? ???? : 
(A) 12 
(B) 7 
(C) 18 
(D) None of these 
Ans: (B) Maximum path difference = 100 nm = 3 . 5 ?? 
So, we can get pd of - 3 ?? , - 2 ?? , … . 3 ?? . 
i.e. 7 maxima. 
 
 
 
Page 2


JEE Solved Example on Wave Optics 
JEE Mains 
Q1:  Two coherent monochromatic light beams of intensities I and 4 I are superposed. The 
maximum and minimum possible intensities in the resulting beam are: 
(A) ?? ?? and I 
(B) 51 and 31 
(C) 9 I and I 
(D) 91 and 31 
 Ans: (C) I = ?? 1
+ ?? 2
+ 2 v ?? 1
?? 2
c o s ? ?? ?? max
? c os ? ?? = 1
I = 9 |
I
mi n
? c os ? ?? = - 1
?? mi n
= ?? 
 
Q2 When light is refracted into a denser medium, 
(A) Its wavelength and frequency both increase 
(B) Its wavelength increase but frequency remains unchanged 
(C) Its wavelength decreases but frequency remain unchanged 
(D) It wavelength and frequency both decrease. 
Ans: (C) ?? =
?? ?? 
In denser medium, c decreases but frequency remains the same. 
? ?? also decreases 
 
Q3: In YDSE how many maxima can be obtained on the screen if wavelength of light used is 
?????? ???? and ?? = ?????? ???? : 
(A) 12 
(B) 7 
(C) 18 
(D) None of these 
Ans: (B) Maximum path difference = 100 nm = 3 . 5 ?? 
So, we can get pd of - 3 ?? , - 2 ?? , … . 3 ?? . 
i.e. 7 maxima. 
 
 
 
Q4:  In Young's double slit experiment, the wavelength of red light is ???????? Å and that of blue is 
???????? Å. The value of ?? for which ?? th 
 bright band due to red light coincides with ( ?? + ?? )
th 
 bright 
band due to blue light is: 
(A) 1 
(B) 2 
(C) 3 
(D) 4 
Ans: (B) 
?? ?? 1
?? ?? =
( ?? + 1 ) ?? 2
?? ?? 
?? ( 2200 ) = ( ?? + 1 ) ( 5200 )
? ? 3 ?? = 2 ( ?? + 1 )
? ? ?? = 2
 
 
Q. 5 Two identical narrow slits ?? ?? and ?? ?? are illuminated by light of wavelength ?? from a point 
source ?? . If, as shown in the diagram above, the light is then allowed to fall on a screen, and if ?? is 
a positive integer, the condition for destructive interference at ?? is 
 
(A) ( ?? 1
- ?? 2
) = ( 2 ?? + 1 ) ?? / 2 
(B) ( ?? 3
- ?? 4
) = ( 2 ?? + 1 ) ?? / 2 
(C) ( ?? 1
+ ?? 2
) - ( ?? 3
+ ?? 4
) = ???? 
(D) ( ?? 1
+ ?? 3
) - ( ?? 2
+ ?? 4
) = ( 2 ?? + 1 ) ?? / 2 
 
 Sol 5: (D) ( ?? 1
+ ?? 3
) - ( ?? 2
+ ?? 4
) =
( 2 ?? + 1 ) ?? 2
? ?
 path by  path by 
?? 1
?? 2
 
 
 
 
 
Page 3


JEE Solved Example on Wave Optics 
JEE Mains 
Q1:  Two coherent monochromatic light beams of intensities I and 4 I are superposed. The 
maximum and minimum possible intensities in the resulting beam are: 
(A) ?? ?? and I 
(B) 51 and 31 
(C) 9 I and I 
(D) 91 and 31 
 Ans: (C) I = ?? 1
+ ?? 2
+ 2 v ?? 1
?? 2
c o s ? ?? ?? max
? c os ? ?? = 1
I = 9 |
I
mi n
? c os ? ?? = - 1
?? mi n
= ?? 
 
Q2 When light is refracted into a denser medium, 
(A) Its wavelength and frequency both increase 
(B) Its wavelength increase but frequency remains unchanged 
(C) Its wavelength decreases but frequency remain unchanged 
(D) It wavelength and frequency both decrease. 
Ans: (C) ?? =
?? ?? 
In denser medium, c decreases but frequency remains the same. 
? ?? also decreases 
 
Q3: In YDSE how many maxima can be obtained on the screen if wavelength of light used is 
?????? ???? and ?? = ?????? ???? : 
(A) 12 
(B) 7 
(C) 18 
(D) None of these 
Ans: (B) Maximum path difference = 100 nm = 3 . 5 ?? 
So, we can get pd of - 3 ?? , - 2 ?? , … . 3 ?? . 
i.e. 7 maxima. 
 
 
 
Q4:  In Young's double slit experiment, the wavelength of red light is ???????? Å and that of blue is 
???????? Å. The value of ?? for which ?? th 
 bright band due to red light coincides with ( ?? + ?? )
th 
 bright 
band due to blue light is: 
(A) 1 
(B) 2 
(C) 3 
(D) 4 
Ans: (B) 
?? ?? 1
?? ?? =
( ?? + 1 ) ?? 2
?? ?? 
?? ( 2200 ) = ( ?? + 1 ) ( 5200 )
? ? 3 ?? = 2 ( ?? + 1 )
? ? ?? = 2
 
 
Q. 5 Two identical narrow slits ?? ?? and ?? ?? are illuminated by light of wavelength ?? from a point 
source ?? . If, as shown in the diagram above, the light is then allowed to fall on a screen, and if ?? is 
a positive integer, the condition for destructive interference at ?? is 
 
(A) ( ?? 1
- ?? 2
) = ( 2 ?? + 1 ) ?? / 2 
(B) ( ?? 3
- ?? 4
) = ( 2 ?? + 1 ) ?? / 2 
(C) ( ?? 1
+ ?? 2
) - ( ?? 3
+ ?? 4
) = ???? 
(D) ( ?? 1
+ ?? 3
) - ( ?? 2
+ ?? 4
) = ( 2 ?? + 1 ) ?? / 2 
 
 Sol 5: (D) ( ?? 1
+ ?? 3
) - ( ?? 2
+ ?? 4
) =
( 2 ?? + 1 ) ?? 2
? ?
 path by  path by 
?? 1
?? 2
 
 
 
 
 
Q. 6 In a young's double slit experiment, a small detector measures an intensity of illumination of I 
units at the centre of the fringe pattern. If one of the two (identical) slits is now covered, the 
measured intensity will be 
(A) 21 
(B) I 
(C) ?? / ?? 
(D) ?? / ?? 
Ans:  (C) Let intensity due to single slit by ?? 1
. By two slits we get I. 
? ?? = ?? 1
+ ?? 2
+ 2 v ?? 1
?? 2
c os ? ( ?? ) 
and ?? = 0
°
 at centre. 
? ? ?? = 4 ?? 1
? ? ?? 1
=
?? 4
 
 
Q. 7 In a Young's double slit experiment ?? equals the distance of screen and ?? is the separation 
between the slit. The distance of the nearest point to the central maximum where the intensity is 
same as that due to a single slit, is equal to 
(A) 
?? ?? ?? 
(B) 
????
?? ?? 
(C) 
????
?? ?? 
(D) 
?? ????
?? 
 
Ans: (C) Let I be intensity due to single slit. 
I = I + I + 2 v I . I c os ? ?? ? ? c os ? ?? =
- I
2I
=
- 1
2
? ? ?? = 120
°
 
Phase difference =
2 ?? 3
 
for 2 ?? ?
????
?? 
for 
2 ?? 3
?
????
3 ?? 
 
 
 
 
Page 4


JEE Solved Example on Wave Optics 
JEE Mains 
Q1:  Two coherent monochromatic light beams of intensities I and 4 I are superposed. The 
maximum and minimum possible intensities in the resulting beam are: 
(A) ?? ?? and I 
(B) 51 and 31 
(C) 9 I and I 
(D) 91 and 31 
 Ans: (C) I = ?? 1
+ ?? 2
+ 2 v ?? 1
?? 2
c o s ? ?? ?? max
? c os ? ?? = 1
I = 9 |
I
mi n
? c os ? ?? = - 1
?? mi n
= ?? 
 
Q2 When light is refracted into a denser medium, 
(A) Its wavelength and frequency both increase 
(B) Its wavelength increase but frequency remains unchanged 
(C) Its wavelength decreases but frequency remain unchanged 
(D) It wavelength and frequency both decrease. 
Ans: (C) ?? =
?? ?? 
In denser medium, c decreases but frequency remains the same. 
? ?? also decreases 
 
Q3: In YDSE how many maxima can be obtained on the screen if wavelength of light used is 
?????? ???? and ?? = ?????? ???? : 
(A) 12 
(B) 7 
(C) 18 
(D) None of these 
Ans: (B) Maximum path difference = 100 nm = 3 . 5 ?? 
So, we can get pd of - 3 ?? , - 2 ?? , … . 3 ?? . 
i.e. 7 maxima. 
 
 
 
Q4:  In Young's double slit experiment, the wavelength of red light is ???????? Å and that of blue is 
???????? Å. The value of ?? for which ?? th 
 bright band due to red light coincides with ( ?? + ?? )
th 
 bright 
band due to blue light is: 
(A) 1 
(B) 2 
(C) 3 
(D) 4 
Ans: (B) 
?? ?? 1
?? ?? =
( ?? + 1 ) ?? 2
?? ?? 
?? ( 2200 ) = ( ?? + 1 ) ( 5200 )
? ? 3 ?? = 2 ( ?? + 1 )
? ? ?? = 2
 
 
Q. 5 Two identical narrow slits ?? ?? and ?? ?? are illuminated by light of wavelength ?? from a point 
source ?? . If, as shown in the diagram above, the light is then allowed to fall on a screen, and if ?? is 
a positive integer, the condition for destructive interference at ?? is 
 
(A) ( ?? 1
- ?? 2
) = ( 2 ?? + 1 ) ?? / 2 
(B) ( ?? 3
- ?? 4
) = ( 2 ?? + 1 ) ?? / 2 
(C) ( ?? 1
+ ?? 2
) - ( ?? 3
+ ?? 4
) = ???? 
(D) ( ?? 1
+ ?? 3
) - ( ?? 2
+ ?? 4
) = ( 2 ?? + 1 ) ?? / 2 
 
 Sol 5: (D) ( ?? 1
+ ?? 3
) - ( ?? 2
+ ?? 4
) =
( 2 ?? + 1 ) ?? 2
? ?
 path by  path by 
?? 1
?? 2
 
 
 
 
 
Q. 6 In a young's double slit experiment, a small detector measures an intensity of illumination of I 
units at the centre of the fringe pattern. If one of the two (identical) slits is now covered, the 
measured intensity will be 
(A) 21 
(B) I 
(C) ?? / ?? 
(D) ?? / ?? 
Ans:  (C) Let intensity due to single slit by ?? 1
. By two slits we get I. 
? ?? = ?? 1
+ ?? 2
+ 2 v ?? 1
?? 2
c os ? ( ?? ) 
and ?? = 0
°
 at centre. 
? ? ?? = 4 ?? 1
? ? ?? 1
=
?? 4
 
 
Q. 7 In a Young's double slit experiment ?? equals the distance of screen and ?? is the separation 
between the slit. The distance of the nearest point to the central maximum where the intensity is 
same as that due to a single slit, is equal to 
(A) 
?? ?? ?? 
(B) 
????
?? ?? 
(C) 
????
?? ?? 
(D) 
?? ????
?? 
 
Ans: (C) Let I be intensity due to single slit. 
I = I + I + 2 v I . I c os ? ?? ? ? c os ? ?? =
- I
2I
=
- 1
2
? ? ?? = 120
°
 
Phase difference =
2 ?? 3
 
for 2 ?? ?
????
?? 
for 
2 ?? 3
?
????
3 ?? 
 
 
 
 
Q7:  A plane wavefront ???? is incident on a concave mirror as shown. 
 
Then, the wavefront just after reflection is 
 
Sol 8: (C) 
 
 
 
 
 
 
 
 
 
 
Page 5


JEE Solved Example on Wave Optics 
JEE Mains 
Q1:  Two coherent monochromatic light beams of intensities I and 4 I are superposed. The 
maximum and minimum possible intensities in the resulting beam are: 
(A) ?? ?? and I 
(B) 51 and 31 
(C) 9 I and I 
(D) 91 and 31 
 Ans: (C) I = ?? 1
+ ?? 2
+ 2 v ?? 1
?? 2
c o s ? ?? ?? max
? c os ? ?? = 1
I = 9 |
I
mi n
? c os ? ?? = - 1
?? mi n
= ?? 
 
Q2 When light is refracted into a denser medium, 
(A) Its wavelength and frequency both increase 
(B) Its wavelength increase but frequency remains unchanged 
(C) Its wavelength decreases but frequency remain unchanged 
(D) It wavelength and frequency both decrease. 
Ans: (C) ?? =
?? ?? 
In denser medium, c decreases but frequency remains the same. 
? ?? also decreases 
 
Q3: In YDSE how many maxima can be obtained on the screen if wavelength of light used is 
?????? ???? and ?? = ?????? ???? : 
(A) 12 
(B) 7 
(C) 18 
(D) None of these 
Ans: (B) Maximum path difference = 100 nm = 3 . 5 ?? 
So, we can get pd of - 3 ?? , - 2 ?? , … . 3 ?? . 
i.e. 7 maxima. 
 
 
 
Q4:  In Young's double slit experiment, the wavelength of red light is ???????? Å and that of blue is 
???????? Å. The value of ?? for which ?? th 
 bright band due to red light coincides with ( ?? + ?? )
th 
 bright 
band due to blue light is: 
(A) 1 
(B) 2 
(C) 3 
(D) 4 
Ans: (B) 
?? ?? 1
?? ?? =
( ?? + 1 ) ?? 2
?? ?? 
?? ( 2200 ) = ( ?? + 1 ) ( 5200 )
? ? 3 ?? = 2 ( ?? + 1 )
? ? ?? = 2
 
 
Q. 5 Two identical narrow slits ?? ?? and ?? ?? are illuminated by light of wavelength ?? from a point 
source ?? . If, as shown in the diagram above, the light is then allowed to fall on a screen, and if ?? is 
a positive integer, the condition for destructive interference at ?? is 
 
(A) ( ?? 1
- ?? 2
) = ( 2 ?? + 1 ) ?? / 2 
(B) ( ?? 3
- ?? 4
) = ( 2 ?? + 1 ) ?? / 2 
(C) ( ?? 1
+ ?? 2
) - ( ?? 3
+ ?? 4
) = ???? 
(D) ( ?? 1
+ ?? 3
) - ( ?? 2
+ ?? 4
) = ( 2 ?? + 1 ) ?? / 2 
 
 Sol 5: (D) ( ?? 1
+ ?? 3
) - ( ?? 2
+ ?? 4
) =
( 2 ?? + 1 ) ?? 2
? ?
 path by  path by 
?? 1
?? 2
 
 
 
 
 
Q. 6 In a young's double slit experiment, a small detector measures an intensity of illumination of I 
units at the centre of the fringe pattern. If one of the two (identical) slits is now covered, the 
measured intensity will be 
(A) 21 
(B) I 
(C) ?? / ?? 
(D) ?? / ?? 
Ans:  (C) Let intensity due to single slit by ?? 1
. By two slits we get I. 
? ?? = ?? 1
+ ?? 2
+ 2 v ?? 1
?? 2
c os ? ( ?? ) 
and ?? = 0
°
 at centre. 
? ? ?? = 4 ?? 1
? ? ?? 1
=
?? 4
 
 
Q. 7 In a Young's double slit experiment ?? equals the distance of screen and ?? is the separation 
between the slit. The distance of the nearest point to the central maximum where the intensity is 
same as that due to a single slit, is equal to 
(A) 
?? ?? ?? 
(B) 
????
?? ?? 
(C) 
????
?? ?? 
(D) 
?? ????
?? 
 
Ans: (C) Let I be intensity due to single slit. 
I = I + I + 2 v I . I c os ? ?? ? ? c os ? ?? =
- I
2I
=
- 1
2
? ? ?? = 120
°
 
Phase difference =
2 ?? 3
 
for 2 ?? ?
????
?? 
for 
2 ?? 3
?
????
3 ?? 
 
 
 
 
Q7:  A plane wavefront ???? is incident on a concave mirror as shown. 
 
Then, the wavefront just after reflection is 
 
Sol 8: (C) 
 
 
 
 
 
 
 
 
 
 
Q9:  In a Young's double slit experiment, first maxima is observed at a fixed point ?? on the screen. 
Now the screen is continuously moved away from the plane of slits. The ratio of intensity at point 
?? to the intensity at point O (center of the screen) 
 
(A) Remains constant 
(B) Keeps on decreasing 
(C) First decrease and then increases 
(D) First decreases and then becomes constant 
Ans: