A double-slit experiment using violet light of wavelength 400 nm produces a spacing of (triangle x). what is expected spacing if red light of wavelength 600 nm used?
a) 2/3 (triangle x)
b) (triangle x)
c) 1.5 (triangle x)
d) 3 (triangle x)
spacing is directly proportional to wavelength , spacing then is
600/400 *triangle ...reduce the fraction.
http://hyperphysics.phy-astr.gsu.edu/hbase/phyopt/slits.html#c1
To find the expected spacing when using red light with a wavelength of 600 nm in the double-slit experiment, we need to compare it to the spacing produced by violet light with a wavelength of 400 nm.
The spacing in the double-slit experiment is determined by the formula:
(spacing) = (wavelength) * (distance between the slits) / (distance to the screen)
Since the distance between the slits and the distance to the screen remain constant, the spacing is directly proportional to the wavelength.
To find the expected spacing, we can divide the wavelength of red light (600 nm) by the wavelength of violet light (400 nm):
(expected spacing) = (wavelength of red light) / (wavelength of violet light)
= 600 nm / 400 nm
= 3/2
Therefore, the expected spacing when using red light is 1.5 times the spacing produced by violet light.
The correct answer is c) 1.5 (triangle x).
To solve this problem, we need to use the formula for calculating the spacing in a double-slit experiment:
Spacing = (wavelength * Distance) / slit_width
In this case, we are given the wavelength of the violet light as 400 nm and the spacing as (triangle x). Let's solve for the original spacing using these values:
Spacing_violet = (400 nm * Distance) / slit_width
Now, we are asked to find the expected spacing if red light with a wavelength of 600 nm is used. Let's denote this as Spacing_red. We can use the same formula as above:
Spacing_red = (600 nm * Distance) / slit_width
To compare the two spacings, we can divide the equation for Spacing_red by the equation for Spacing_violet:
Spacing_red / Spacing_violet = [(600 nm * Distance) / slit_width] / [(400 nm * Distance) / slit_width]
The slit width and the distance between the slits and the screen are the same for both cases (violet and red light), so they cancel out:
Spacing_red / Spacing_violet = 600 nm / 400 nm = 1.5
Therefore, the expected spacing using red light will be 1.5 times the spacing obtained with violet light. Looking at the given options, we can see that the correct answer is:
c) 1.5 (triangle x)