The distance y3,red from the center of the pattern to the location of the third diffraction minimum of the red laser is 4.05 cm. How far L is the screen from the slit

L = a 1,929 10⁴ m

a = 0.1 mm = 0.1 10⁻³ m,     L = 1,929 m

Explanation:

The diffraction phenomenon is described by the expression

       a sin θ = m λ

Let's use trigonometry to find the breast

        tan θ = y / x

As the angles are very small

       tan θ = sin θ/ cos θ = sin θ = y / x

We replace

        a y / L = m λ

        L = a y / m λ

The red light has a wavelength of Lam = 700 nm = 700 10⁻⁹ m, in the third pattern it is m = 3

       L = a  4.05 10⁻² / (3 700 10⁻⁹)

       L = a 1,929 10⁴ m

To give a specific value we must know the width of the slit, suppose a value of  a = 0.1 mm = 0.1 10⁻³ m

       L = 1,929 m

this means that the temperature of both substances will be equal