Single Slit Diffraction

Question

Monochromatic light of wavelength 500 nm passes through a single slit of width 0.1 mm, so what is the angular position of the first diffraction minimum?

RankGuru · Accepted Answer

In single slit diffraction, NCERT gives the condition for the dark fringes as $a\sin	heta=m\lambda$, where $a$ is the slit width, $\lambda$ the wavelength, and $m$ the order of the minimum. For the first minimum $m=1$, and for small angles $\sin	heta\approx	heta$, so $	heta\approx\frac{\lambda}{a}$. Substituting $\lambda=500	imes10^{-9}$ m and $a=0.1	imes10^{-3}=10^{-4}$ m gives $	heta\approx\frac{500	imes10^{-9}}{10^{-4}}=\frac{5	imes10^{-7}}{10^{-4}}=5	imes10^{-3}$ radian, or 0.005 radian. The value 0.05 radian is wrong because it misplaces the slit-width exponent by one order. The value 0.0025 radian is wrong because it halves the correct result, perhaps confusing the central maximum half-width incorrectly. The value 0.5 radian is wrong because it is far too large for such a narrow-wavelength-to-width ratio. As stated in NCERT Class 12, Chapter 10, the central maximum broadens as the slit narrows, since $	heta$ scales as $\lambda/a$. A magnitude check confirms that a slit two hundred times wider than the wavelength gives a small angle of a few milliradians, consistent with 0.005 radian.

Single Slit Diffraction

Select the correct option:

🔒 Solution Hidden from View

More optics Practice Questions

A single slit of width 0.1 mm is illuminated by parallel light of wavelength 500 nm, and the diffrac...

A patient can see distant objects clearly but struggles to focus on nearby print, and an optometrist...

An astronomer wants a telescope to distinguish two closely spaced stars more clearly, and a student ...

A ray of light passes through a rectangular glass slab with parallel faces immersed in air, and a st...

Two independent ordinary light bulbs placed side by side never produce a stable interference pattern...

During the daytime the clear sky overhead appears blue to observers on the ground, and a curious lea...

Unpolarized light of intensity I0 passes first through an ideal polarizer and then a second polarize...

An astronomical telescope in normal adjustment uses an objective of focal length 100 cm and an eyepi...

A biconvex lens is ground from glass of refractive index 1.5 with both surfaces having a radius of m...

A compound microscope achieves high magnification by combining two convex lenses, and a laboratory s...

A thin converging lens forms a sharp image on a screen placed 40 cm away when a candle stands 40 cm ...

Two thin lenses of powers +5 D and -2 D are placed in contact along the same axis, and an optician w...

About This Question

Solution