Ray Optics - Optical Instruments

Optical Instruments

Optical instruments are devices that are used to processes light waves to enhance an image for viewing, or analyze light waves to determine one of a number of characteristic properties. The first optical instrument invented was telescope and was used for magnification of distant images, and microscopes used for magnifying very tiny images. 

Simple Microscope

It is an optical instrument used to see very small objects. It's magnifying power is given by

m = Visual angle with instrument (β)/Visual angle when object is placed at least distance of distinct vision(α)

Simple microscope

(i) It is a single convex lens of lesser focal length.

(ii) Also called magnifying glass or reading lens.

(iii) Magnification's, when final image is formed at D and ∞

     (i.e. m_D and m_∞)    m_D = (1 + D/f)_max

     and       m_∞ = (D/f)_min

(iv) If lens is kept at a distance a from the eye then m_D = 1 + D – a /f and m_∞ = D–a/f

Compound Microscope

(i) Consist of two converging lenses called objective and eye lens.

(ii) f_{eye lens} > f_objective and (diameter)_{eye lens} > (diameter)_objective

(iii) Intermediate image is real and enlarged.

(iv) Final image is magnified, virtual and inverted.

(v) u_o = Distance of object from objective(o), v_o = Distance of image (A'B') formed by objective from objective, u_e = Distance of A'B' from eye lens, v_e = Distance of final image from eye lens, f_o = Focal length of objective, f_e = Focal length of eye lens.

(vi) Final image is formed at D: Magnification m_D = – v_o/u_o (1+ D/f_e) and length of the microscope tube (distance between two lenses) is L_D = v_o + u_e.

Generally object is placed very near to the principal focus of the objective hence u_o = f_o. The eye piece is also of small focal length and the image formed by the objective is also near to the eye piece.

So v_o = L_D, the length of the tube.

Hence, we can write m_D = –L/d_o (1+ D/f_e)

(vii) Final image is formed at ∞: magnification m∞ = –v_o/u_o.D/f_e and length of tube L∞ = v_o + f_e

      In terms of length m∞ = (L_∞ – f_o – f_e)D/f_o f_e

(viii) For large magnification of the compound microscope, both f_o and f_e should be small.

(ix) If the length of the tube of microscope increases, then its magnifying power increases.

(x) The magnifying power of the compound microscope may be expressed as M = m_o × m_e; where m_o is the magnification of the objective and m_e is magnifying power of eye piece.

Astronomical Telescope

By astronomical telescope heavenly bodies are seen.

(i) f_objective >; f_{eye lens} and d_objective >; d_{eye lens}

(ii) Intermediate image is real, inverted and small.

(iii) Final image is virtual, inverted and small.

(iv) Magnification: m_D = –f_o/f_e (1+f_e/D) and m_∞ = –f_o/f_e

(v) Length : L_D = f_o+ u_e and L_∞ = f_o + f_e

Resolving Limit and Resolving Power

Microscope: In reference to a microscope, the minimum distance between two lines at which they are just distinct is called Resolving limit (RL) and it's reciprocal is called Resolving power (RP)

λ = Wavelength of light used to illuminate the object,

µ = Refractive index of the medium between object and objective,

θ = Half angle of the cone of light from the point object,

µ sin θ = Numerical aperture.

Telescope: Smallest angular separations (dθ) between two distant objects, whose images are separated in the telescope is calledresolving limit. So revolving limit dθ = 1.22λ/a and resolving power  where a = aperture of objective.