In ydse if width of slits arebin the ratio 4:9 the ratio of the intensity of madima to intensity at minima will be
Answers
Answer:
The ratio of the minimum and maximum intensity is \dfrac{1}{4}
4
1
.
Explanation:
Given that,
The slit widths are in the ratio 1 : 9,
We know that,
Width is directly proportional to the intensity
\dfrac{\beta_{1}}{\beta_{2}}=\dfrac{I_{1}}{I_{2}}
β
2
β
1
=
I
2
I
1
\dfrac{I_{1}}{I_{2}}=\dfrac{1}{9}
I
2
I
1
=
9
1
The intensity is directly proportional to square of the amplitude.
\dfrac{I_{1}}{I_{2}}=(\dfrac{A_{1}^2}{A_{2}^2})
I
2
I
1
=(
A
2
2
A
1
2
)
\dfrac{A_{1}}{A_{2}}=\dfrac{1}{3}
A
2
A
1
=
3
1
The maximum intensity is
I_{max}=(A_{1}+A_{2})^2I
max
=(A
1
+A
2
)
2
I_{max}=(1+3)^2I
max
=(1+3)
2
I_{max}=16I
max
=16
The minimum intensity is
I_{min}=(A_{1}-A_{2})^2I
min
=(A
1
−A
2
)
2
I_{min}=(1-3)^2I
min
=(1−3)
2
I_{min}=4I
min
=4
The ratio of the minimum and maximum intensity will be
\dfrac{I_{min}}{I_{max}}=\dfrac{A_{2}}{A_{1}}
I
max
I
min
=
A
1
A
2
\dfrac{I_{min}}{I_{max}}=\dfrac{4}{16}
I
max
I
min
=
16
4
\dfrac{I_{min}}{I_{max}}=\dfrac{1}{4}
I
max
I
min
=
4
1
Hence, The ratio of the minimum and maximum intensity is \dfrac{1}{4}
4
1
.
Explanation:
please mark it as brainlist