Using monochromatic light of 410 nm wavelength, a single thin slit forms a diffraction pattern, with the first minimum at an angle of 40.0° from central maximum. The same slit, when illuminated by a new monochromatic light source, produces a diffraction pattern with the second minimum at a 60.0° angle from the central maximum. What is the wavelength of this new light? a. 256 nm b. 283 nm c. 307 nm d. 329 nm e. none of these

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Physics

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6 August, 14:23

Using monochromatic light of 410 nm wavelength, a single thin slit forms a diffraction pattern, with the first minimum at an angle of 40.0° from central maximum. The same slit, when illuminated by a new monochromatic light source, produces a diffraction pattern with the second minimum at a 60.0° angle from the central maximum. What is the wavelength of this new light? a. 256 nm b. 283 nm c. 307 nm d. 329 nm e. none of these

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Herman · Answer 1

c. 307 nm

Explanation:

angular position of first dark fringe = λ / d, λ is wavelength and d is width of slit.

(40 x π) / 180 = 410 / d

angular position of second dark fringe = 2 x λ / d, λ is wavelength and d is width of slit.

(60 x π) / 180 = 2 x λ / d

Dividing these equations

60 / 40 = 2 x λ / 410

λ = 307.5 nm.