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

ok

explanation:

when jerome paddle in flowing river towards east the net speed of jerome will increase

so the net speed of jerome will be given as

now the speed of paul will be same as it is given as he is running on the ground

so

so here we can say since the speed of jerome is more so he will win the race

now as we know the distance so the time difference is given as

so jerome will reach first and the time difference will be 203.55 s or 3.4 min