Question

White light is incident on a glass plate of thickness $5000\mathring{A}$ and refractive index $1.5$. The wavelength in the visible region $(4000\mathring{A}-7000\mathring{A})$ that is strongly reflected by the plate is

• A. $4290\mathring{A}$
• B. $8000\mathring{A}$
• C. $4000\mathring{A}$
• D. $5000\mathring{A}$

Answer 1

Answer: (A)

Light of wavelength $l$ is strongly reflected if
$2\mu t=\left(2n+1\right)\frac{\lambda }{2}...\left(i\right)$
If $\lambda =4000\mathring{A},n=3.25$
If $\lambda =7000\mathring{A},n=1.66$
Hence, within $4000\mathring{A}$ and $7000\mathring{A}$ the integer can take values $2$ and $3$. (from eq. (i)).
Putting $n=3$, we get
$\lambda =4290\mathring{A}$
Hence option is $\lambda =4290\mathring{A}$