Calculating the Angle of Diffraction: A Step-by-Step Guide

Understanding how to calculate the angle of diffraction is a fundamental skill for anyone delving into the world of A Level Physics. You might wonder, why does this matter? Well, diffraction plays a vital role in technologies like lasers, telecommunications, and even fiber optics. With that in mind, let’s jump into a practical example that’s bound to make everything clearer.

Lay the Groundwork: The Grating Equation

To tackle the problem, we need to lean on the grating equation:

[ d \sin(\theta) = m \lambda ]

This equation might seem intimidating initially, but it's just a recipe for finding our answer. Let’s break it down:

• ( d ) represents the grating spacing.
• ( m ) is the order of diffraction, which tells us which "peak" of light we are considering—in this case, the second order.
• ( \lambda ) denotes the wavelength of the light passing through.
• ( \theta ) is our target— the angle of diffraction.

Getting to the Numbers

Now, let's run through our specific values for this example:

• The wavelength, ( \lambda ), is given as 590 nm (nanometers), which converts to ( 590 \times 10^{-9} ) m—yes, a bit of unit conversion magic helps here!
• The grating spacing ( d ) is ( 1.67 \times 10^{-6} ) m.
• The order ( m ) is 2, as we are focusing on the second-order beam.

Time to Calculate!

Substituting these values into our grating equation gives us:

[ 1.67 \times 10^{-6} \sin(\theta) = 2 \times (590 \times 10^{-9}) ]

Now, let’s do a little math. The right-hand side simplifies to:

[ 2 \times (590 \times 10^{-9}) = 1180 \times 10^{-9} = 1.18 \times 10^{-6} , \text{m} ]

Now we have:

[ 1.67 \times 10^{-6} \sin(\theta) = 1.18 \times 10^{-6} ]

Here's where the magic happens. We need to isolate ( \sin(\theta) ):

[ \sin(\theta) = \frac{1.18 \times 10^{-6}}{1.67 \times 10^{-6}} ]

Let’s calculate that quotient:

[ \sin(\theta) \approx 0.706 ]

What’s the Angle?

Now, we need to find ( \theta ). This is where a little trigonometry comes into play. To find ( \theta ), take the arcsin (inverse sine):

[ \theta = \arcsin(0.706) ]

When you work that out (and yes, a calculator here is your best friend), you find:

[ \theta \approx 45^\circ ]

Voila!

And there you have it! The angle of diffraction for the second order diffracted beam is 45 degrees. So if you had been pondering between options A, B, C, and D, you’d be right to choose B.

Wrapping It Up

This example not only sharpened your math skills but also illustrated a core concept of wave behavior that you'll encounter in various applications. Keep practicing similar problems, and these concepts will become second nature.

If you're preparing for your A Level Physics exam, focusing on these types of calculations will be immensely helpful. Remember, physics isn’t just numbers; it’s the language of the universe. Embrace it, and you’ll find that things begin to fall into place. Ready for more challenges? Let’s navigate through the fascinating world of physics together!