(This article is based on Astroproject -2 “LIMB DARKENING OF SUN’ BY’ S N Tandon published in the newsletter of IUCAA Khagol – April 1993)
To the unaided eye, the Sun appears as a disk of uniform brightness. The Sun is so bright that it is not possible to look at it for more than a fraction of a second, except at grave risk to the eyes.
To have a better look at the solar disk, you could use two or three layers of aluminium coated Mylar sheets to reduce its intensity. If you carefully look at the Sun through these sheets, the regions near the edge or limb of the Sun would appear darker.
The relative darkness of the solar limb is not due to lack of spherical symmetry, but it is caused due to the radial temperature gradient near the surface. That is decrease in temperature from center to the edge of the solar disk.
Sun can be considered as a gaseous sphere at high temperature; the well-defined boundary is seen because the light can penetrate only a very tiny fraction of the Sun, unlike in the case of a usual terrestrial flame which is penetrated deeply by light.
If the light penetrates a distance λ then the light we receive from the centre of the solar disk would have arisen from layers between radii ro and (ro – λ), ro being the solar radius. On the other hand, if we look close to the limb, the light reaching us would have arisen from layers of radii between ro and (ro – λ^2/2ro) (see Fig. 1) below.
As λ << ro, it is clear that while looking near the limb, we are receiving light from relatively outer layers of the solar atmosphere. As the temperature of the outer layers is lower, the light received from the limb has a lower intensity. This ‘darkening’ effect is shown in Fig. 2 for different wavelengths of light; it can be seen that the effect is larger for smaller wavelengths, being maximum for blue light in the visible region.
To get sharp images achromatic lenses are necessary — ordinary single lenses have different focal lengths for different colours and therefore give rise to unsharp coloured images. Just to demonstrate the limb darkening effect one can reduced this defect by placing a blue (red) plastic film in front of the telescope, and by reducing the opening of the objective lens through the use of a cardboard cover with a 1 – 3 cm diameter hole in it.
For taking measurements of solar limb darkening measurements you need to project the image of the Sun. Visit these links below for projecting solar image.
- Poor man’s telescope
- My First telescope
- Projecting solar image – using telescope
- Coelostate – IUCAA model
When this project was first written we had used a photosensitive resister and also a photometer. But now you can use various app on you mobile that measure light brightness.
I am using Light meter app from Physics Toolbox by Vieyra Software . Their latest app is Physics Toolbox Suit which has many other options such as (Kinematics – g-Force meter, Gyroscope etc.) Acoustics (Sound Meter, tone Detector etc.) and Ling (Light meter, Color Detector, etc.). This app stores data in <dot>csv format. The file then can be analysed using MSExcel software.
DIYA 