Question

In a double-slit experiment it is found that blue light ofwavelength 467 nm gives a second-order maximum at a certainlocation on the screen. What wavelength of visible light would havea minimum at the same location?

Answer 1

In a double-slit experiment, the wavelength of visible light that would have a minimum at the same location as a second-order maximum of blue light with a wavelength of 467 nm can be calculated using the relationship: wavelength_min = (2 * path difference) / odd_multiple. By substituting the path difference corresponding to the blue light's second-order maximum into the equation, we can find the wavelength of visible light that would have a minimum at the same location.

Step-by-step explanation:

In a double-slit experiment, the spacing between the slits determines the interference pattern formed on the screen. When blue light of wavelength 467 nm gives a second-order maximum at a certain location on the screen, it means that the path difference between the two slits is half the wavelength of the light. To find the wavelength of visible light that would have a minimum at the same location, we need to consider the path difference between the slits for a minimum. In a double-slit interference pattern, a minimum occurs when the path difference is equal to an odd multiple of half the wavelength. Therefore, the wavelength of visible light that would have a minimum at the same location can be obtained by using the relationship:

wavelength_min = (2 * path difference) / odd_multiple

Since we are given the wavelength of blue light (467 nm) that resulted in a second-order maximum, we can calculate the path difference by multiplying the wavelength by the order number:

path difference = wavelength_blue * order_number

Substituting the values of the given blue light wavelength and order number:

path difference = 467 nm * 2 = 934 nm

Now, we can substitute the calculated path difference into the formula to find the wavelength of visible light that would have a minimum at the same location:

wavelength_min = (2 * 934 nm) / odd_multiple

We can choose any odd number for the odd_multiple to find one of the possible wavelengths that would have a minimum at the same location. For example, if we choose an odd_multiple of 3:

wavelength_min = (2 * 934 nm) / 3 = 1245.3 nm

So, a wavelength of approximately 1245.3 nm of visible light would have a minimum at the same location as the second-order maximum of blue light with a wavelength of 467 nm.

Answer 2

To find the wavelength of visible light that would have a minimum at the same location as the second-order maximum of blue light in a double-slit experiment, you can rearrange the formula sin(θ) = mλ/d. By plugging in the values and solving, you can determine the wavelength to be 0.0500 mm.

Step-by-step explanation:

In a double-slit experiment, the location of the maximums and minimums of light depends on the wavelength of the light and the separation between the slits. The formula for finding the angle of the maximums and minimums is given by:

sin(θ) = mλ/d

Where θ is the angle, m is the order of the maximum or minimum, λ is the wavelength, and d is the separation between the slits.

In this question, the given wavelength of the blue light is 467 nm, and it produces a second-order maximum at a certain location on the screen. To find the wavelength of visible light that would have a minimum at the same location, we can rearrange the formula:

λ = d * sin(θ) / m

Since we want a minimum, the order will be 1. Plugging in the values, we get:

λ = (0.0500 mm) * sin(θ) / 1

Therefore, the wavelength of the visible light that would have a minimum at the same location is 0.0500 mm.