# Estimating the wavelength of light using a double-slit and a plane diffraction grating

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Introduction

Title

Estimating the wavelength of light using a double-slit and a plane diffraction grating

Objective

To project a Young’s interference pattern on a screen and make measurements to estimate the wavelength of light

To estimate the wavelengths of the different colours of the spectrum produced using a fine diffraction grating

Apparatus

Instrument | Descriptions |

1 double slit | Mounted on a large cardboard |

1 translucent screen | Ground glass |

1 Compact light source | With vertical filament |

1 Low voltage power supply | ------------------------------------------------- |

1 Magnifying glass | ------------------------------------------------- |

2 metre rule | 100 cm |

1 vernier caliper | Smallest division 0.1mm |

1 diffraction grating | 3000 lines per cm |

1 ray-box | Without lens and slit plate |

Theory

Using a double-slit

In the Young’s double slit experiment, two rays through the slits interfere to give the interference pattern. Bright fringes occur at positions where constructive interference occurs (Fig.1). The path difference from the slits at an angle θ is a multiple n of the wavelength λ, i.e.

a sin θ=nλ,

where n=1,2,3… is known as order number.

For small value of θ,

Sinθ= tanθ= s/D

Where s is

Middle

- A ‘T’ with 2 metre rules was formed

and it was pointed towards

a ray-box 1 to 2 metres away (Fig 4).

- A diffraction grating was held against one end of a metre rule. The vertical filament of the ray-box lamp was viewed through the grating. A diffraction pattern consisting of the first and second order spectra would be seen.(Fig 5)

- A pencil was moved along the second metre rule until it was in line with the middle of the blue colour of the first order spectrum. The distance x was measured.

- From x, tanθ and then sinθ were found. The grating formula λ=dsinθ was applied to calculate the wavelength of the light.

- Steps 9 and 10 were repeated with the green and red colours in turn and the wavelength of the different colours were calculated.

Results and discussion

Using a double-slit

- Calculate the wavelength of light using the formula λ=ay/D.

Slit separation a = 0.3 mm

Fringe separation y/mm (4 fringes measured) | 3.4/4=0.85 | 4.18/4=1.045 | 5.5/4=1.375 |

Slit-to screen distance D/m | 0.46 | 0.6 | 0.7 |

Wavelength λ=ay/D | 554x10-9 | 523x10-9 | 589x10-9 |

Conclusion

-There are errors from fringe separation reading using vernier caliper.

Maximum error = 0.1/2=0.05mm

For example, the first reading of y is actually 0.85+0.1mm

So the wavelength obtained is not accurate.

For the diffraction grating experiment,

-It is difficult to locate the exact fringe for that particular colour.

-There are errors from readings of x using a metre rule.

Maximum error = 0.1/2=0.05cm

Reading of x for 1st order green fringe is actually 0.17+0.001m

So the wavelength obtained is not accurate.

- In this experiment, the first order spectrum is used foe measuring he wavelengths of different colors. Give one advantage and disadvantage of using the second order spectrum instead.

The advantage is that the angular separation of second order is larger than that of first order. It will have a smaller measurement percentage error.

The disadvantage is that the intensity of the second order is lower and the corresponding fringes for each colour are difficult to locate.

Safety precaution

-The light source is very hot. Hold it with care.

Reference

Tao, Lee & Mak’s A-Level Practical Physics Third Edition (Oxford).P.72-75

This student written piece of work is one of many that can be found in our AS and A Level Waves & Cosmology section.

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