Light of wavelength $$6000 \mathop A\limits^o$$ is incident on a thin glass plate of r.i. 1.5 such that the angle of refraction into the plate is $$60^{\circ}$$. Calculate the smallest thickness of the plate which will make dark fringe by reflected beam interference.

In a single-slit diffraction experiment, the slit is illuminated by light of two wavelengths $$\lambda_1$$ and $$\lambda_2$$. It is observed that the $$2^{\text {nd }}$$ order diffraction minimum for $$\lambda_1$$ coincides with the $$3^{\text {rd }}$$ diffraction minimum for $$\lambda_2$$. Then

A ray of monochromatic light is incident on the plane surface of separation between two media $$\mathrm{X}$$ and $$\mathrm{Y}$$ with angle of incidence '$$\mathrm{i}$$' in medium $\mathrm{X}$ and angle of refraction 'r' in medium Y. The given graph shows the relation between $$\sin \mathrm{i}$$ and $$\sin \mathrm{r}$$. If $$\mathrm{V}_{X}$$ and $$\mathrm{V}_{Y}$$ are the velocities of the ray in media X and Y respectively, then which of the following is true?

X-rays of wavelength $$\lambda$$ gets reflected from parallel planes of atoms in a crystal with spacing d between two planes as shown in the figure. If the two reflected beams interfere constructively, then the condition for maxima will be, (n is the order of interference fringe)