A single slit forms a diffraction pattern, with the first minimum at an angle of 40 degrees from central maximum. Monochromatic light of 410 nm wavelength is used. The same slit, illuminated by a different monochromatic light source, produces a diffraction pattern with the second minimum at a 60 degree angle from the central maximum. The wavelength of this light, in nm, is closest to:

276.19nm

Explanation:

To find the other wavelength you use the following condition for the diffraction of both wavelengths:

   ( 1 )

λ1=410nm

m=1 for wavelength 1

m=2 for wavelength 2

a: width of the slit

θ1: angle of the first minimum

θ2: angle of the second minimum

you divide both equations and you obtain:

hence, the wavelength of the second monochromatic wave is 276.19nm

The wavelength of the  second monochromatic light is  

Explanation:

From the question we are told that

    The angle of the first minimum is

   The wavelength of the first  monochromatic light is  

    The angle of the second minima is  

For the first minima the distance of separation of diffraction patterns is mathematically represented as

 Substituting values

The distance between two successive diffraction is constant for the same slit

  Thus the wavelength of the second light is

 Substituting value

the first, second, and fifth options