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 of something to make a distinct shadow with blue light of frequency 6.7 x 10^14 Hz, we can use the formula:

Width = (10 * wavelength) / sin(theta)

Where:
- Width is the narrowest width of the object
- Wavelength is the wavelength of the blue light
- Theta is the angle of diffraction

To find the wavelength of blue light, we can use the formula:

Wavelength = speed / frequency

Applying this formula, we get:

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

Now, we can substitute the values into the width formula:

Width = (10 * 4.48 x 10^-7 m) / sin(theta)

Unfortunately, the problem does not provide the value of the angle of diffraction (theta), so we cannot find the exact value of the narrowest width without this information.

Moving on to the second part of the question, we need to determine if the shadow would be more or less distinct when illuminated by red light with a frequency of 4.2 x 10^14 Hz.

Following a similar approach as before, we find the wavelength of the red light:

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

Now, we can use the same formula to calculate the width:

Width_red = (10 * 7.14 x 10^-7 m) / sin(theta)

Comparing the value of Width_red with that of Width (obtained for blue light earlier), we can determine if the shadow would be more or less distinct. If Width_red is greater than Width, the shadow would be less distinct under red light illumination. If Width_red is less than Width, the shadow would be more distinct under red light illumination.