Sizes: Using a pinhole camera to measure the Sun or Moon

Things to find out• What happens to the size of the image as you move the sheet of paper or screen furtheraway from the pinhole, but keep the candle in the same place?__Image will get larger and fainter _______________________________________• Try drawing a graph of image height (vertical axis) against the distance of the paper orscreen from the pinhole camera (horizontal axis).• Look at your graph – what do you think it tells you?• For each pair of measurements, calculate the result when you divide the height of theimage by the distance between the camera and the screen or paper.• Multiply the result of the division calculations by the distance between the candle and thepinhole camera.Height of image cm× ·distance between the candle and the pinhole cmDistance to screen from pinhole cm= _________________________ cm = Height of the candle flame or light source• Measure the height of your candle flame or light source.My light source is _____________________cm highHow similar are the your two values for the height of the light source _________________You should find that the graph is a straight line, because the height of the image is directlyproportional to the distance between the image and the pinhole.You should also find that all the divisions give the same result (and that this is the same as thegradient of the graph.• Multiply the result of the division calculations by the distance between the candle or otherlight source and the pinhole camera.• This should give you the height of the actual candle flame or light source – check to seehow accurate the value is2. Finding the diameter of the Sun or Moon.It is very important that no one looks directly at the sun, as this will damage the retina inthe eye. The pinhole camera is a safe way to observe the sun, since you only need tolook at the image on thescreen, not directly at it.• Black out a window that facesthe Sun or Moon, and cut asquare about 2cm x 2cm inthe centre of the blackoutmaterial.• Put the foil over the squarehole and tape it to theblackout material.• Use a pin or similar to make asmall hole in the foil.Dr Lisa Jardine-Wright, Cavendish Laboratory December 2007

• Turn out all the lights in the room.• Hold a sheet of white paper or a screen as far from the pinhole as possible.• You should now be able to see an image of the Sun or Moon on the paper or screen – if itisn’t clear enough, try blacking out more windows to reduce the light in the room orexperiment with the size of your pinhole.• Measure accurately and record the distance between the pinhole and the white paper orscreen.The distance between my image and the pinhole camera was ______________ cm.• Measure accurately and record the diameter of your images of the Sun or Moon (using thesame units).The diameter of my Sun or Moon image is ______________ cm.• Now we will calculate the real diameter of the Sun or Moon from your measurements.Calculation• The diameters of the moon and the cut-out semi-circle are in the same proportion as thedistances between your eye and the moon and between your eye and the window.DiameterDistance from Earth of Sun or Moon × Diameterof Sun or Moon =Distance to Screen from Pinholeof Image• The distance of the Earth from the Sun is 149,600,000km• The distance of the Earth from the Moon is 384,400 km• You will need to make sure that you change all your distance measurements to the sameunits, e.g. metres.o Remember there are 100cm in 1m and 1000m in 1km.• Fill in the blanks in the boxes below (example measurements)Diameterof_ MOON_ in km =384,400km ×1201.1cmcmDiameter of _MOON_ in km =3523kmORDiameterof_ SUN_ in km =149,600,000km ×1201.1cmcmDiameter of _SUN_ in km =1,371,333kmDr Lisa Jardine-Wright, Cavendish Laboratory December 2007

Things to think about• How many times bigger is the Sun than the Moon?Diameter of SUNin kmDiameter of MOONin km=1,371,3333,523≈ 390• Why do you think that they appear to be about the same size to us?Because the Sun is about 390 times further away than the moonNotes:Distance of SUN from Earth in kmDistance of MOON from Earth in km=149,600,000384,400≈ 390The calculation of relative sizes when using a pinhole camera relates to the method of similartriangles:• In the diagram on the right the redlines show the path of the light raysfrom the Sun or Moon through thepinhole onto the screen.• Note that the image is upside down,compared with the object – thiswon’t show up easily for the Sun orMoon but should be evident for thecandle.• The two triangles AOB and COD aresimilar, although not the same size(the same shape with a common,equal angle at the apex).• This means that:AB CD=XO OYAB = CD ×XOOYDr Lisa Jardine-Wright, Cavendish Laboratory December 2007