When light of a certain wavelength is incident normally on a certain diffraction grating the line of order 1 is at a diffraction angle of 25 degrees. The diffraction angle of the second order line is :

a) 25
b) 42
c) 50
d) 58
e) 75

I am not sure how to do this problem since it does not have enough information to use the diffraction equations in the book. So, I do not know how to handle the problem.

Thank you

n lambda = d sin( theta )
Since the order n doubles from 1 to 2, so does the sine of the diffraction angle. Find the angle that has twice the sine of 25 degrees. It is not 50 degrees.

d) 58

you said find the angle that is double sin25 (not sin50)

so 2 x sin 25 gets you .84523

find what angle that is using inverse sin

sin^-1 (.84523) = 57.697

Well, well, well! Looks like we have a little diffraction mystery on our hands. Don't worry, I, your trusty Clown Bot, am here to solve it with a side of humor!

Now, let's zoom into this problem. We know that the diffraction angle for the first order line is 25 degrees. But what about the second order line? It's like trying to find the second star in a star-studded sky!

But fear not, my friend! Remember the diffraction equation, n lambda = d sin(theta)? In this case, since the order n doubles from 1 to 2, we are looking for an angle with twice the sine of 25 degrees.

So, let's double the sine of 25 degrees and see where it takes us! Drumroll, please... It's not 50 degrees! That would be too easy!

Instead, you'll find that the diffraction angle of the second order line is... *drumroll intensifies*... 58 degrees! That's right, option D is the lucky winner!

So remember, my dear friend, when it comes to diffraction grating, always trust in the power of doubling sine angles and a sprinkle of clown humor. Good luck with your physics adventures!

To determine the diffraction angle of the second-order line, we need to use the relationship between the order of the line (n), the wavelength of light (λ), the spacing between the grating lines (d), and the diffraction angle (θ).

The formula is given as:
nλ = d * sin(θ)

Given that the diffraction angle of the first-order line is 25 degrees, we can plug in the values to the equation:
1 * λ = d * sin(25)

To find the diffraction angle of the second-order line, we need to consider that the order (n) doubles. Therefore, we need to find the angle that has twice the sine of 25 degrees.

sin(2θ) = 2 * sin(θ)
sin(2θ) = 2 * sin(25)
sin(2θ) = 2 * (sin(25))

To determine the value of sin(2θ), we need to find the angle whose sine is equal to 2 * sin(25). We can use a calculator to find this value, which is approximately 0.8268.

Therefore, the diffraction angle of the second-order line is the angle whose sine is equal to 0.8268. Using the inverse sine function (sin^(-1)), we can find this angle.

θ = sin^(-1)(0.8268)

Using a calculator to find the inverse sine of 0.8268, we get approximately 56.37 degrees.

Therefore, the diffraction angle of the second-order line is approximately 56.37 degrees, which is closest to option d) 58 degrees.

To find the diffraction angle of the second-order line, we can use the equation nλ = d sin(θ), where n is the order of the line, λ is the wavelength of light, d is the spacing between the slits in the diffraction grating, and θ is the diffraction angle.

Given that the first-order diffraction angle (θ₁) is 25 degrees, we need to find the second-order diffraction angle (θ₂).

Since the order n doubles from 1 to 2, the sine of θ₂ will also double. So, we need to find the angle that has twice the sine of 25 degrees.

sin(θ₂) = 2 * sin(25 degrees)

To find the angle that has twice the sine of 25 degrees, we can use the inverse sine function:

θ₂ = sin^(-1)(2 * sin(25 degrees))

Using a calculator, you can find:

θ₂ ≈ 58 degrees

Therefore, the diffraction angle of the second-order line is 58 degrees.

The correct answer is option d) 58.