Answer
(a) $648nm$
(b) closer together
Work Step by Step
(a) We can find the required wavelength as follows:
$y=Ltan\theta$
$\implies \theta=tan^{-1}(\frac{y}{L})$
$\implies \theta=tan^{-1}(\frac{23\times 10^{-3}m}{1.20m})$
$\theta=1.1^{\circ}$
Now $dsin\theta=m\lambda$
This can be rearranged as:
$\lambda=\frac{dsin\theta}{4}$
We plug in the known values to obtain:
$\lambda=\frac{(135\times 10^{-6}m)(1.1^{\circ})}{4}$
$\lambda=647.9\times 10^{-9}m=648nm$
(b) We know that if the frequency is increased, then the wavelength decreases because frequency and wavelength are inversely proportional. Thus, due to the decrease in wavelength, the angle between the fringes decreases. Thus, due to the increasing frequency, the bright spots of the pattern move closer together.
