$A$ zone plate of focal length $60\,cm$ behaves as a convex lens. If the wavelength of incident light is $6000\,\mathring{A},$ then the radius of the first half-period zone will be:

  • A
    $36 \times 10^{-8}\,m$
  • B
    $6 \times 10^{-8}\,m$
  • C
    $\sqrt{6} \times 10^{-8}\,m$
  • D
    $6 \times 10^{-4}\,m$

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The solar spectrum during a complete solar eclipse is

Column $I$ shows four situations of standard Young's double slit arrangement with the screen placed far away from the slits $S_1$ and $S_2$. In each of these cases $S_1 P_0 = S_2 P_0$,$S_1 P_1 - S_2 P_1 = \lambda / 4$ and $S_1 P_2 - S_2 P_2 = \lambda / 3$,where $\lambda$ is the wavelength of the light used. In the cases $B, C$ and $D$,a transparent sheet of refractive index $\mu$ and thickness $t$ is pasted on slit $S_2$. The thicknesses of the sheets are different in different cases. The phase difference between the light waves reaching a point $P$ on the screen from the two slits is denoted by $\delta(P)$ and the intensity by $I(P)$. Match each situation given in Column $I$ with the statement$(s)$ in Column $II$ valid for that situation.
Column $I$Column $II$
$(A)$ No sheet$(p)$ $\delta(P_0) = 0$
$(B)$ $(\mu-1)t = \lambda / 4$$(q)$ $\delta(P_1) = 0$
$(C)$ $(\mu-1)t = \lambda / 2$$(r)$ $I(P_1) = 0$
$(D)$ $(\mu-1)t = 3\lambda / 4$$(s)$ $I(P_0) > I(P_1)$
$(t)$ $I(P_2) > I(P_1)$

Statement $(S)$: Using Huygen's eye-piece,measurements can be taken but are not correct.
Reason $(R)$: The cross wires,scale,and final image are not magnified proportionately because the image of the object is magnified by two lenses,whereas the cross-wire scale is magnified by one lens only.
Identify the correct option from the following:

Choose the incorrect statement.

$A$ carrot looks orange in colour because of the $\beta$-carotene molecule in it. This means that the $\beta$-carotene molecule absorbs light of wavelengths

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