Final answer:
The width of the diffraction maximum for light with a wavelength of 460 nm is calculated using a ratio based on the given width for 580 nm light. The result is 4.76 cm.
Step-by-step explanation:
To find the width of the diffraction maximum for light with a wavelength of 460 nm, we can use the relationship between the width of the maximum, the distance to the screen, and the wavelength. The width of the maximum is directly proportional to the wavelength when the distance to the screen and the slit size are constant. The width of the diffraction maximum (W) can be calculated using the formula:
W = λ × (L / d)
where λ is the wavelength of the light, L is the distance to the screen, and d is the width of the slit.
Given that the original width of the maximum (W580) is 6.0 cm for 580 nm light, and the distance to the screen (L) is 2.20 m, we can set up a ratio with the new wavelength λ460 (460 nm):
W460 / W580 = λ460 / λ580
Plugging in the given values, we get:
W460 / 6.0 cm = 460 nm / 580 nm
Which simplifies to:
W460 = (460/580) × 6.0 cm
W460 = 4.76 cm
Thus, the width of the diffraction maximum for 460 nm light will be 4.76 cm.