Question

Assertion :In YDSE, if I${}_1=9I_0$ and l${}_2=4I_0$ then $\frac{I_{max}}{I_{min}}$ = 25 Reason: In YDSE I${}_{max}=(\sqrt{I_1}+\sqrt{I_2}{)}^2$ and $(\sqrt{I_1}-\sqrt{I_2}{)}^2$

• A. Both Assertion and Reason are correct but Reason is the correct explanation for Assertion
  
• B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
• C. Assertion is correct but Reason is incorrect
• D. Both Assertion is incorrect but Reason is correct

Answer 1

The correct option is A Both Assertion and Reason are correct but Reason is the correct explanation for Assertion

For interference between two intensities,

$I=I_1+I_2=2\sqrt{I_1{I}_2}cos\delta$

For maximum intensity, $\delta =2n\pi$

$⟹I_{max}=I_1+I_2+2\sqrt{I_1{I}_2}=(\sqrt{I_1}+\sqrt{I_2}{)}^2$

For minimum intensity,

$⟹I_{min}=I_1+I_2-2\sqrt{I_1{I}_2}=(\sqrt{I_1}-\sqrt{I_2}{)}^2$

Hence the reason is correct.

If $I_1=9I_0,I_2=4I_0$

$I_{max}=25I_0$, $I_{min}=I_0$

Hence, $\frac{I_{max}}{I_{min}}=25$