Physics - Geometrical Optics Question with Solution | TestHub

Working of a simple microscope (magnifying glass): An object AB is seen by the eye lens. The length A'B' of the image formed on the retina by the eye lens is dependent on 'θ' because radius of the eye is constant for a person during observation of an object R ≈ 1.25 cm. An object of fixed height will appear to be of different heights as seen from different distances because of different values of 'θ'. Stars are of very large size but they appear to be very small because they are at very-very large distances. 'θ' is called angle of vision or visual angle.

For larger 'θ', the object will appear larger, θ depends on both 'h' and 'd'. If 'θ' is very small then the object is not visible to us. To increase 'θ' the object should be kept nearest to the eye but then the object cannot be seen clearly because in that case the eye lens cannot adjust its focal length to make the image on the retina. The objects infront of the eye can have a minimum distance 'D' from the eye for their image to be formed on retina. 'D' is called LEAST DISTANCE OF CLEAR VISION. D ≈ 25 cm for average grown-up person. If an object is kept from distance 'D' to '∞' from a defect free eye then its image can be formed on retina and it will be clearly visible. Sometimes an object kept in this range forms a very small angle and hence cannot be seen like dust particles, bacteria etc. To increase their 'θ' microscope (for small object near the eye) or telescope (for large objects but far away) is used. A simple microscope is a converging lens (for example lens used by watch repairer). The image formed by this lens acts as the object for the eye. Their performance is represented by a parameter called 'angular magnification' or 'magnifying power'. It is represented by 'm':

$m=\frac{\theta }{{\theta }_{max}}$

here θ = angle of vision of the image formed by the optical instrument (like microscope or telescope); θmax = maximum angle of vision that an object can subtend on the eye when no optical instrument is used (for example if the object is kept at 'D' then the 'θ' is maximum). For this passage we will assume that eye is a thin lens at the front of the eye.