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Two spectral lines, incident on a grating of grating element $a+b$ have wavelengths $\lambda$ and $\lambda+ d \lambda$ respectively.For normal incidence, the angular separation between these lines in $n^{th}$ order must be
$\frac{n d \lambda}{(a+b)- n \lambda}$
$\frac{n d \lambda}{\sqrt{(a+b)^2+ n^2 \lambda^2}}$
$\frac{n d \lambda}{\sqrt{(a+b)^2- n^2 \lambda^2}}$
$\frac{n d \lambda}{(a+b)^2- n^2 \lambda^2}$
A parallel beam of monochromatic light of wavelength $4000A^o$ is incident normally on a grating of grating element length $15000A^o$. The angular dispersion of the diffracted beam in the third order spectrum must be
$3.34 \times 10^{-1} rad/A^o$
$3.34 \times 10^{-2} rad/A^o$
$3.34 \times 10^{-3} rad/A^o$
$3.34 \times 10^{-4} rad/A^o$
In the fraunhoffer diffraction pattern formed by a single slit, the slit width is $0.04 cm$ and wawveleingth of light used is $5000 A^o$. The diffraction angle for the first dark fringe must be
$1.25 \times 10^{-3} rad$
$2.25 \times 10^{-3} rad$
$3.25 \times 10^{-3} rad$
$4.25 \times 10^{-3} rad$
A convex lens of focal length 25 cm is placed after a slit of width 0.5 mm . If a plane wave of wavelength $5000 A^o$ falls on the slit normally, then, the separation between the second minima on either side of the central maximum of the diffraction pattern,would be
$1.0 \times 10^{-3}$
$1.5 \times 10^{-3}$
$2.0 \times 10^{-3}$
$2.5 \times 10^{-3}$
Fringes are seen within the shadow of a thin wire held vertically in front of a narrow slit illumnated by light of wavelength $5000 A^o$. If the fringe width at a distance of 3 m is 1.5 mm, the diameter of the wire has to be
0.5 mm
1 mm
1.5 mm
2 mm
When a circular aperature of 1.5 mm radius is illuminated by a plane wave of light, the most intense point on the axis is at a distance of 350 cm from the aperature. The wavelength of the incident light must be
$4428.5 A^o$
$5428.5 A^o$
$6428.5 A^o$
$7428.5 A^o$
A zone plate of focal length 21 cm is illuminated by light of wavelength $4200 A^o$. The radius of the $11^{th}$ zone of the zone plate must be
$58.48 \times 10^{-5} m $
$78.48 \times 10^{-5} m $
$98.48 \times 10^{-5} m $
$118.48 \times 10^{-5} m $
A grating having 4500 lines per cm is illuminated by a light of wavelength $4000 A^o$. The highest order of the spectrum , that will be visible , will be
5
6
3
4
The pattern of netwton rings formed between a plane glass plate and a convex lens of focal length180 cm , is used as a zone plate. The principal focal length of the zone plate will be
2.8 m
1.8 m
4.8 m
3.8 m
The image of a point source of light of wavelength $4800 A^o$ at a distance of 1.2 m from the zone plate is observed at 2.0 m on the other side. The focal lenth of the zone plate must be
