# A confusion about the use of telescope

Suppose we are measuring wavelength of a light with the help of spectrometer and a grating. Spectrometer consists of three main parts: Collimator, Turntable, Telescope. Grating is placed on turn table. We can obtain diffraction pattern on a screen instead of a telescope. Then why do we go for telescope? What are benefits of using telescope over using a simple screen to view fringes?

I am assuming a standard sort of experiment done in a teaching laboratory.

The collimator produces a beam of parallel light which passes through the grating and then onward into the telescope which focussed at infinity or onto a screen.

The theory which links the wavelength of the line to the angle assumes that light to and from the grating is parallel can achieved using a telescope in a relative small space whereas with a screen a much larger area for the experiment would be needed.

The first thing which be noted is that the lines seen through the telescope are much brighter than those seen on the screen and so many more lines can be seen when viewed through the telescope than can be seen on the screen.
To see the fainter lines on a screen would require a darkened room and a waiting time for eyes to adapt.

With a telescope the angle is measured by setting the cross wires on the line whose wavelength is to be found and an angle measured using a vernier scale which even using a fairly cheap spectrometer can measure to one minute of arc $(\frac{1}{60}^\circ \approx 0.017^\circ)$.
To achieve such an accuracy of angle measurement using a screen is very difficult and would have to be done using trigonometry.
If the angle to be measured was $30^\circ$ and the grating was $1.000\,\rm m$ from the screen this would correspond to a distance between the straight through position and the $30^\circ$ position of 577 mm. An error of $1\,\rm mm$ in the measurement of that distance would result in an error in the angle of approximately $0.04^\circ$. And then do not forget the error in measure the metre distance between the grating (where do you start) and the screen. I doubt if an accuracy of a quarter of a degree can be achieved.
Moving the screen further away will induce the intensity of the lines and the measurement of distance more difficult.

For demonstration purposes the spectral lines formed on a screen and measuring the wavelength of the light approximately is useful but for reasonable accurate and simple measurements of wavelength the telescope wins out.

The telescope magnifies the spectrum allowing measurements with greater angular resolution. If you have a very big screen a good distance away, in a large dark room it could achieve similar, but this is less practical.

• And, more generally, any optical arrangement to transfer an image plane from one place to another, with or without magnification or demagnification, is called a telescope. Usually the context is clear to distinguish between a telescope for looking at stars and a telescope to move beams around an optical bench. – Jon Custer Jan 24 '17 at 15:14