Diffraction of light-Wave Optics

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Question

In a single slit diffraction experiment first minimum for red light (660 nm) coincides with first maximum of some other wavelength $λ^{'}$ . The value of $λ^{'}$ in (nm)

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Solution

$I n a \sin g l e s l i t d i f f r a c t i o n e x p e r i m e n t, p o s i t i o n o f m i n i m a i s g i v e n b y d \sin θ = n λ . S o f o r f i r s t m i n i m a o f r e d \sin θ = 1 \times (\frac{λ_{R}}{d}) a n d a s f i r s t m a x i m a i s m i d w a y b e t w e e n f i r s t a n d s e c o n d m i n i m a, f o r w a v e l e n g t h λ^{'}, i t s p o s i t i o n w i l l b e d \sin θ^{'} = \frac{λ^{'} + 2 λ^{'}}{2} \Rightarrow \sin θ^{'} = \frac{3 λ^{'}}{2 d} A c c o r d i n g t o g i v e n c o n d i t i o n, \sin θ = \sin θ^{'} \Rightarrow λ^{'} = \frac{2}{3} λ_{R} λ^{'} = \frac{2}{3} \times 660 = 440 n m$

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Diffraction of light-Wave Optics

Remember concepts with our Masterclasses.

In a single slit diffraction experiment first minimum for red light (660 nm) coincides with first maximum of some other wavelength λ' . The value of λ' in (nm)

Ready to Test Your Skills?

free study material

In a single slit diffraction experiment first minimum for red light (660 nm) coincides with first maximum of some other wavelength $λ^{'}$ . The value of $λ^{'}$ in (nm)