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  4. White light is incident on a glass plate of thickness 5000 mathringA and refractive index 1.5. The wavelength in the visible region (4000 mathringA - 7000 mathringA) that is strongly reflected by the plate is

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Q. 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

Wave Optics

Solution:

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 $\lambda = 4290\,\mathring{A}$