## Diffraction gratings and patterns

Posted in AQA AS Unit 2, AS Unit 2: Waves by Mr A on 21 Feb 2010

Diffraction grating equation

Important: The following derivation assumes that all rays incident on each part of the screen are parallel. This is a fair assumption, provided the distance from the slits to the screen is much larger than the slit separation.

Thus, for the central fringe, the rays travel exactly the same distance as one another.

For the first order fringe, each successive ray travels an extra path difference of $d \sin{\theta}$. Incidentally, this extra path difference must also be equal to $\lambda$, for constructive interference to occur.

If we proceed to the second order fringe, each successive ray must travel an extra $n \lambda$. It, therefore, follows that

$\boxed{n \lambda = d \sin{\theta}}$

Worked example (class demo)

If a red laser is shone through a diffraction grating with ? lines per mm at a screen ? m away, and the first order fringe makes an anlge of ?, what is the wavelength of the light?

## Interference and Diffraction

Posted in AQA AS Unit 2, AS Unit 2: Waves by Mr A on 20 Feb 2010

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## Focussing with a Convex Lens

Posted in AQA AS Unit 2, AS Unit 2: Waves by Mr A on 14 Feb 2010
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## Huygens’ Principle and Wavefronts

Posted in AQA AS Unit 2, AS Unit 2: Waves by Mr A on 7 Feb 2010

• Huygens’ principle
• Diffraction and Reflection
• Refraction

Huygens’ Principle

Given that waves are caused by a source of disturbance, and that waves themselves cause disturbance as they propagate, Christiaan Huygens (1629-1695) treated waves along the principle that:

Every point on a wave may be considered as a point source disturbance, causing secondary waves that spread out evenly in all directions with a speed equal to the speed of propagation of the wave.

Diffraction and Reflection

1)

2)

3)

Refraction

## Optical Fibres

Posted in AQA AS Unit 2, AS Unit 2: Waves by Mr A on 31 Jan 2010
• What are optical fibres?
• Why use them?
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## Finding the Critical Angle

Posted in AQA AS Unit 2, AS Unit 2: Waves by Mr A on 22 Jan 2010
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## Snell’s Law, Refraction and Total Internal Reflection

Posted in AQA AS Unit 2, AS Unit 2: Waves by Mr A on 13 Jan 2010

When light meets the boundary between two media it is either refracted or reflected. What happens depends on the refractive indices of the media and the angle of incidence.

$n_{1} \sin \theta_{1} = n_{2} \sin \theta_{2}$

• $n_{1}$ = refractive index of incident medium
• $n_{2}$ = refractive index of refractive medium
• $\theta_{1}$ = angle of incidence
• $\theta_{2}$ = angle of refraction

Special Cases

1) $n_{1} < n_{2}$

$\Rightarrow \sin \theta_{1} > \sin \theta_{2}$

$\Rightarrow \theta_{1} > \theta_{2}$

So, even at maximum incident angle,

$\theta_{1} = 90 \quad \Rightarrow \quad \theta_{2} < 90$

This means that the ray is always refracted.

2) $n_{1} > n_{2}$

$\Rightarrow \sin \theta_{2} > \sin \theta_{1}$

$\Rightarrow \theta_{2} > \theta_{1}$

Therefore, when the incident angle, $\theta_{1}$, is above some critical angle $\theta_{c}$,

$\theta_{1} > \theta_{c} \quad \Rightarrow \quad \theta_{2} > 90$

So, if the angle of incidence is large enough (larger than the critical angle), the ray will not be refracted, but instead reflect off the boundary. This is known as total internal reflection (TIR).

 Snell’s Law Applet

 Note on Refraction

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## Waves Questions 1

Posted in AQA AS Unit 2, AS Unit 2: Waves by Mr A on 9 Jan 2010

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Answers to this worksheet

## Introduction to Waves

Posted in AQA AS Unit 2, AS Unit 2: Waves by Mr A on 7 Jan 2010

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Transverse and longitudinal waves, sometimes called s-waves and p-waves respectively, are demonstrated in these videos. Transverse waves oscillate perpendicular to the direction of motion, and longitudinal waves oscillate in the direction of motion.

Frequency, Wavelength and Wave Speed

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Extras