An optical filter passes only far red light with an average wavelength of 6500 Å. (1 Å = 10-10 m). Calculate

Question

Visualize a highly detailed cross-section of an optical filter allowing only far red light to pass through. Display the light particles as they encounter the filter, with only those corresponding to the wavelength of 6500 Å managing to traverse. It should be vividly colored to represent the color spectrum, highlighting the red spectrum especially. Draw a ruler besides the pass through light to suggest measurement, but avoid any text. No human figures are needed in this image.

An optical filter passes only far red light with an average wavelength of 6500 Å. (1 Å = 10-10 m). Calculate

(a) the wavelength in centimeters.
(b) the frequency.

Answer 1

Convert 6500 A to meters then to cm.

Then c = fw
c is speed of light in m/s
f = frequency in Hz
w = wavelength in m
Post your work if you get stuck.

Answer 2

(a) To convert the wavelength from Ångstroms (Å) to centimeters (cm), we can use the conversion factor 1 Å = 10^-10 m.

Given that 1 cm = 10^-2 m, we can set up a conversion factor:

1 Å = 10^-10 m = x cm

To find x, we multiply both sides of the equation by the conversion factor from meters to centimeters:

1 Å * (1 cm/10^-2 m) = 10^-10 m * (1 cm/10^-2 m)

Simplifying, we find:

x = 10^-10 m * 10^2 cm

x = 10^-10 * 10^2 cm

x = 10^-10+2 cm

x = 10^-8 cm

Therefore, the wavelength in centimeters (cm) is 10^-8 cm.

(b) To calculate the frequency, we can use the formula:

frequency (ν) = speed of light (c) / wavelength (λ)

The speed of light is approximately 3 x 10^8 m/s.

Converting the wavelength from Ångstroms (Å) to meters (m), we use the conversion factor 1 Å = 10^-10 m:

wavelength (λ) = 6500 Å * (10^-10 m/1 Å)

Simplifying, we find:

wavelength (λ) = 6500 * 10^-10 m

Now we can substitute the values into the formula:

frequency (ν) = (3 x 10^8 m/s) / (6500 * 10^-10 m)

First, simplify the denominator:
frequency (ν) = (3 x 10^8 m/s) / (6.5 * 10^-6 m)

To divide by a decimal in the denominator, we multiply the numerator and denominator by a power of 10 to remove the decimal:

frequency (ν) = (3 x 10^8 m/s) * (10^6 / 6.5)

Simplifying, we find:

frequency (ν) = 3 x 10^8 * 10^6 / 6.5

Using the properties of exponents, we add the exponents:

frequency (ν) = 3 x 10^14 / 6.5

frequency (ν) ≈ 4.615 x 10^13 Hz

Therefore, the frequency is approximately 4.615 x 10^13 Hz.

Answer 3

To solve this problem, we can use the relation between wavelength, frequency, and the speed of light. The speed of light is a constant value of approximately 3 x 10^8 meters per second.

(a) To convert the wavelength from angstroms (Å) to centimeters (cm), we can use the conversion factor: 1 Å = 10^-8 cm.

So, the wavelength in centimeters can be calculated as follows:
Wavelength in cm = (Wavelength in Å) x (Conversion factor)
Wavelength in cm = 6500 Å x 10^-8 cm/Å
Wavelength in cm = 6500 x 10^-8 cm
Wavelength in cm = 6.5 x 10^-5 cm

Therefore, the wavelength in centimeters is 6.5 x 10^-5 cm.

(b) To calculate the frequency, we can use the formula:
Frequency = Speed of light / Wavelength

Frequency = (3 x 10^8 m/s) / (Wavelength in meters)

First, let's convert the wavelength in angstroms to meters using the conversion factor: 1 Å = 10^-10 m.

Wavelength in meters = Wavelength in Å x (Conversion factor)
Wavelength in meters = 6500 Å x 10^-10 m/Å
Wavelength in meters = 6500 x 10^-10 m
Wavelength in meters = 6.5 x 10^-7 m

Now we can calculate the frequency:
Frequency = (3 x 10^8 m/s) / (6.5 x 10^-7 m)
Frequency = 4.615 x 10^14 Hz

Therefore, the frequency is approximately 4.615 x 10^14 Hz.