Intensity at a point on the screen

[HelpPlease27]

Homework Statement

Monochromatic light of wavelength 592 nm from a distant source passes through a slit that is 0.0290 mm wide. In the resulting diffraction pattern, the intensity at the center of the central maximum (θ = 0∘) is 3.00×10−5 W/m2 .
What is the intensity at a point on the screen that corresponds to θ = 1.20∘?
Express your answer with the appropriate units.

Homework Equations

$$I = I_0[\sin(\pi*a*\sin(\theta)/\lambda)/(\pi*a*\sin(\theta)/\lambda)]^2$$

The Attempt at a Solution

I used the formula and values and got an answer of 1.13*10^-9 W/m^2 but it says it's incorrect and I'm not sure why.

 

[haruspex]

In these forums you need to double the dollar (or hash) signs:
$I = I_0[\sin(\pi*a*\sin(\theta)/\lambda)/(\pi*a*\sin(\theta)/\lambda)]^2$

 

[HelpPlease27]

In these forums you need to double the dollar (or hash) signs:
$I = I_0[\sin(\pi*a*\sin(\theta)/\lambda)/(\pi*a*\sin(\theta)/\lambda)]^2$

Thanks. Changed it

 

[haruspex]

I used the formula and values and got an answer of 1.13*10^-9 W/m^2

I get a number an order of magnitude greater. Any possible confusion between degrees and radians?

 

[HelpPlease27]

I get a number an order of magnitude greater. Any possible confusion between degrees and radians?

Maybe but then do I need to change the 1.2 into radians or i don't know

 

[haruspex]

Maybe but then do I need to change the 1.2 into radians or i don't know

I assume you are using a calculator. Most or all calculators allow you to enter the angle in either degrees or radians, but you have to select the right option. Whichever way you do the inner sine (sin(θ) in the quoted equation), the result of (πa sin(θ)/λ) is in radians.

 

[HelpPlease27]

I assume you are using a calculator. Most or all calculators allow you to enter the angle in either degrees or radians, but you have to select the right option. Whichever way you do the inner sine (sin(θ) in the quoted equation), the result of (πa sin(θ)/λ) is in radians.

Ok, I tried it again and I'm now getting 3.47*10^-10

 

[haruspex]

Ok, I tried it again and I'm now getting 3.47*10^-10

Then you need to post your full working.
I get sin(1.2^o)=0.021, πa/λ=154, multiplying gives 3.22, sine of that is -0.08, dividing by 3.22 gives -0.026, squaring to 0.00067, then multipying by I₀ ends with 2 10^-8W/m².

 

[HelpPlease27]

Then you need to post your full working.
I get sin(1.2^o)=0.021, πa/λ=154, multiplying gives 3.22, sine of that is -0.08, dividing by 3.22 gives -0.026, squaring to 0.00067, then multipying by I₀ ends with 2 10^-8W/m².

Thanks, that makes sense now. Who knows what I was doing in my calculations.