One guideline for how diffraction affects shadows is that distinct shadows are created if the width of something is a minimum of 10 times greater than the wave’s wavelength. What would be the narrowest width of something to make a distinct shadow with blue light of frequency = 6.7 X 10^14 Hz? At this particular width, would the shadow be more or less distinct if it is lit up with red light of frequency 4.2 X 10^14 Hz? Consider the speed to be 3.0 X 10^8 m/s in both parts.

Question

One guideline for how diffraction affects shadows is that distinct shadows are created if the width of something is a minimum of 10 times greater than the wave’s wavelength. What would be the narrowest width of something to make a distinct shadow with blue light of frequency = 6.7 X 10^14 Hz? At this particular width, would the shadow be more or less distinct if it is lit up with red light of frequency 4.2 X 10^14 Hz? Consider the speed to be 3.0 X 10^8 m/s in both parts.

Answer 1

To determine the narrowest width that would create a distinct shadow with blue light, we need to find the wavelength of the blue light first, using the formula:

wavelength = speed of light / frequency.

Given that the speed of light is 3.0 x 10^8 m/s and the frequency of the blue light is 6.7 x 10^14 Hz, we can calculate the wavelength as follows:

wavelength = (3.0 x 10^8 m/s) / (6.7 x 10^14 Hz)
= 4.48 x 10^-7 m.

Now that we have the wavelength of the blue light, we can calculate the minimum width required for a distinct shadow by multiplying the wavelength by 10:

minimum width = 10 x wavelength
= 10 x 4.48 x 10^-7 m
= 4.48 x 10^-6 m.

Therefore, the narrowest width of something to make a distinct shadow with blue light is 4.48 x 10^-6 meters.

Now let's analyze whether the shadow would be more or less distinct if it is lit up with red light of frequency 4.2 x 10^14 Hz. To determine this, we need to compare the width of the object to the red light's wavelength.

Similarly, we can calculate the wavelength of the red light:

wavelength_red = (3.0 x 10^8 m/s) / (4.2 x 10^14 Hz)
= 7.14 x 10^-7 m.

Comparing this wavelength to the minimum width of the object (4.48 x 10^-6 meters), we can see that the width of the object is larger than the red light's wavelength.

Since the width of the object is greater than the red light's wavelength, the shadow with red light would be less distinct compared to the blue light. This is because, when the width of an object is larger than the wavelength of light, diffraction effects become more prominent, causing less defined shadows.