The Spectrometer

A Spectrometer is an optical device used to study spectra from different sources of light.  

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         For the measurement of properties of light such as the wavelength and intensity, over a particular portion of the electromagnetic spectrum, Spectrometer is used. The field of physics in which spectral lines are produced using a diffraction grating along with the spectrometer in order to examine the spectrum of light is called spectroscopy. The typical spectrometer can be operated over a wide range of wavelengths from γ rays and X-rays to infrared but usually spectrometers are used to study the visible spectrum.

With the help of a spectrometer, the deviation of light by a glass prism and refractive index of the material of the prism can be measured quite accurately. Using diffraction grating, the spectrometer can be employed to measure the wavelength of the light.

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Terrestrial Telescope

As astronomical telescope forms inverted final images of heavenly bodies like moon and stars which are acceptable. But when terrestrial objects are to be viewed, it is necessary to have an erect final image. The erection of image can be made by introducing a third lens between objective and eye-piece of telescope.
This modified telescope is known as "Terrestrial Telescope" whose magnifying power is just equal to the magnification of astronomical telescope but it just gives erect image.  

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      Terrestrial telescope contains three lenses as compared to the astronomical telescope. It is also known as the spyglass. As astronomical telescope forms an inverted image of the object so, the main difference between the astronomical and terrestrial telescope is the erection of the final image with respect to the object. The third lens of short focal length f is placed at 2f which forms inverted image of the object. This image serves as the object for the eye-piece. The lens placed in the center of the telescope which actually erects the image is called as the Erecting lens. The resolving power of the telescope can be given by the relations as follows:

Where,

fo = Focal length of the objective lens

fe = Focal length of the eye-piece lens

f = Focal length of lens placed between objective and eye-piece i.e. Erecting lens

  Ray diagram for Terrestrial Telescope

Images for Terrestrial Telescope

Astronomical Telescope

An optical instrument, which is used to see the heavenly objects like moon, stars etc.  

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      The word 'Telescope' is composed of two words 'Tele' and 'Scope'. Tele means very far and Scope means view so, the telescope is an optical instrument used to observe distinct objects.

Astronomical Telescope is an optical instrument by which we can observe heavenly objects like moon, planets, stars etc.

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Construction

         Astronomical Telescope consist of two convex lenses called objective and eye-piece fitted at the ends of two hollow metallic tubes in which one can move inside the other one.

         The objective has large focal length and aperture whereas eye-piece has small focal length and aperture as shown in the figure:

Ray diagram for Astronomical Telescope

Working

       Parallel light rays coming from distant object are converged by objective at its focus and a real but inverted, diminished image IQ is formed at the focus of the objective. 

       The length of the telescope is so adjusted that the IQ may come at the focus of the eye-piece rather just inside the focus of eye-piece and hence virtual and much magnified image I'Q' is formed by the eye-piece at infinity as shown in the above ray diagram.

        The final image formed by astronomical telescope is inverted, virtual and highly magnified.

Magnification

        The magnifying power of the telescope is given by,

                                      

Where are the visual angles subtended by the object and image respectively.

From the above figure, in right angled triangle ∆IX1Q 

For small angle,

where fo is the focal length of objective lens.

In right angled triangle ∆IX2Q,

or,

where fe is the focal length of eye-piece lens.

Putting the values of in equation(1) we get,

or,

      This shows that for high magnification the focal length of the objective should be very large as compared to that of eye-piece.

       The length of telescope is the distance between objective and eye-piece.

Images for Astronomical Telescope

Power and Aberration of Lenses

The reciprocal of focal length of lens is called Power of lens i.e.


The defect (Blurring and distortion) in the image formed by lenses is due to two common reasons i.e. spherical aberration and chromatic aberration. These are known as Lens Aberrations or defects of lens.  

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      The reciprocal of focal length of a lens is its power. The greater the focal length, the lesser will be the power of lens and smaller the focal length, the greater will be the power of lens.

In case of combination of two lenses,

       This shows that the power of combination of two lenses in contact is equal to the sum of their individual powers.

Unit

        The unit of power of lens is "Diopter" and it is defined as the reciprocal of focal length in meters.

i.e.

Defects of Lenses or Lens Aberrations

1-Spherical Aberration

       When rays of light parallel to the principal axis of a lens pass through zones near its edges, these are brought to focus nearer the lens than those rays which pass through region nearer to its center. Therefore, the focus is not a sharp point but is contained in a region called "focal region". This produces blurred images. This problem is known as spherical aberration as shown in figure:

  Fig   Spherical Aberration

Minimizing

• By using only central portion of the lens. This can be achieved by using a stop on the lens which makes effective aperture of the lens small.

• By making opposite surface of the lens of different curvatures.

• By combining a strongly convergent lens of producing little spherical aberration in the opposite direction.

2-Chromatic Aberration

      The fact that different wavelengths of light refracted by lens focus at different points give rise to chromatic aberration as shown in figure:

  Fig   Chromatic Aberration

       Actually a thick lens may be regarded as made up of two prisms placed one above the other and due to dispersion of the refracting medium of the lens different wavelength of light focus at different points. Hence image formed by lens consists of small linear spectrum. Chromatic aberration for a diverging lens is opposite to that for a converging lens.

Minimizing

• This defect can be reduced to a large extent by combining a converging lens of crown glass with a diverging lens of flint glass. These lenses are so chosen that the dispersion of one is equal and opposite to that the other. Lenses which are free from dispersion are called "Achromatic lenses".

Combination of Thin Lenses

The image of an object can be made erect and much magnified by using more than one lenses. Therefore suitable combination of lenses are used in high powered optical instruments.

the above expression is for the combination of two lenses where f1 is the focal length of one lens and f2 is the focal length of the other.  

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      In most of the optical instruments two or more lenses are used in combination. The location, size and nature of the final image can be determined by using lens formula or ray diagram. In either case, we locate first the image formed by the first lens. Using that image as the object for the second lens, the final image formed by the second lens can be located. If there are more than two lenses. This process is continued, the object for each lens is the image for the preceding lens as in the figure below:

  Fig     Showing a combination of thin lenses

       Referring to the above figure, we can see that lens L1 forms an image I1. This image acts as a real object for the lens L2, which forms a real image I2. Notice that I2 is inverted with respect to I1 and erect with respect to the object.

       We now consider the case when the two thin lenses are in contact, which means their separation is very small as compared to their focal lengths. This is illustrated in figure below:

      Let a point object O be placed at a distance p from the lens L1 whose real image I1(in fig I2) is formed by it at a distance q1(in fig q2). From the lens formula,

                                   

Where f1 is the focal length of lens L1.

      This image now serves as a virtual object for the second lens L2 of focal length f2. If we neglect the small separation between the lenses. The distance of this virtual object from lens L2 will be the same as its distance from the lens L1. If the lens forms an image I of this virtual object at a distance q.

                                   

As the object is virtual for lens L2 i.e. P2 = q1,

Adding equation(1) and (2) we get,

Or,

                                   

Now if we replace the two lenses of focal lengths f1 and f2 by single lens of focal length f such that it forms an image at a distance q of an object placed at p from it as shown in figure below, such a lens is called equivalent lens, and its focal length is known as equivalent focal length.

For equivalent lens L, we have

                                   

Comparing equation(3) and (4) we get,

                                    

      This close combination behaves as a single lens whose focal length is given by the above relation.

        The equation(5) shows that for a pair of lenses in contact the sum of the reciprocals of their individual focal lengths is equal to the reciprocal of the focal length of the combination.