Question

1.

A pane of glass is spray painted so as to be opaque; then, a razor is used to create one slash 0.50mm wide through the paint. what is the width of the middle bright spot if a laser light of wavelength 650nm passes through the slash on to a wall 2.0m from the slash.

2.

A toaster filament dissipates 100W when plugged into a 130V outlet; assuming a constant filament resistance, what is the power dissipated by the filament when the toaster is when plugged into a 120V outlet.

Answer 1

1) The width of the central bright spot in single slit diffraction is

$w=\frac{2L\lambda}{a}$

where L = 2 m

lambda = is the wavelength of the light

a = slit width = 0.5 mm

$w=\frac{2\times 2\times 650\times 10^{-9}}{0.5\times 10^{-3}}=0.0052\,\,m=5.2\,\,mm$

2) The resistance of the filament is

$R=V^2/P=130^2/100=169\,\Omega$

The power dissipated by the filament when the toaster is when plugged into a 120 V outlet is

$P=V^2/R=120^2/169=85.21\,\,W$