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A spectroscopic instrument can resolve two nearby wavelengths λ and λ + Δλ if λ/Δλ is smaller than 8000. This is used to study the spectral lines of the Balmer series of hydrogen. Approximately how many lines will be resolved by the instrument?
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Unpolarised light is passed through a polaroid P1. When this polarised beam passes through another polaroid P2 and if the pass axis of P2 makes angle θ with the pass axis of P1, then write the expression for the polarised beam passing through P2. Draw a plot showing the variation of intensity when θ varies from 0 to 2π.
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The current is drawn from a cell of emf E and internal resistance r connected to the network of resistors each of resistance r as shown in the figure. Obtain the expression for
- the current draw from the cell and
- the power consumed in the network.

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Why should the objective of a telescope have large focal length and large aperture? Justify your answer.
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A electron of mass me revolves around a nucleus of charge +Ze. Show that it behaves like a tiny magnetic dipole. Hence prove that the magnetic moment associated wit it is expressed as `vecμ =−e/(2 m_e)vecL `, where `vec L` is the orbital angular momentum of the electron. Give the significance of negative sign.
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Draw a ray diagram depicting the formation of the image by an astronomical telescope in normal adjustment.
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You are given the following three lenses. Which two lenses will you use as an eyepiece and as an objective to construct an astronomical telescope ? Give reason
| Lenses | Power (D) | Aperture (cm) |
| L1 | 3 | 8 |
| L2 | 6 | 1 |
| L3 | 10 | 1 |
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A thin conducting spherical shell of radius R has charge Q spread uniformly over its surface. Using Gauss’s law, derive an expression for an electric field at a point outside the shell.
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Draw a graph of electric field E(r) with distance r from the centre of the shell for 0 ≤ r ≤ ∞.
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Which of the following properties shows that light is a transverse wave?
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An astronomical telescope is to be designed to have a magnifying power of 50 in normal adjustment. If the length of the tube is 102 cm, find the powers of the objective and the eyepiece.
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The eyepiece of an astronomical telescope has a focal length of 10 cm. The telescope is focussed for normal vision of distant objects when the tube length is 1.0. m. Find the focal length of the objective and the magnifying power of the telescope.
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A Galilean telescope is 27 cm long when focussed to form an image at infinity. If the objective has a focal length of 30 cm, what is the focal length of the eyepiece?
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A lady cannot see objects closer than 40 cm from the left eye and closer than 100 cm from the right eye. While on a mountaineering trip, she is lost from her team. She tries to make an astronomical telescope from her reading glasses to look for her teammates. (a) Which glass should she use as the eyepiece? (b) What magnification can she get with relaxed eye?
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A charge Q is placed at the centre of a cube. Find the flux of the electric field through the six surfaces of the cube.
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Consider the following two statements:-
(A) Kirchhoff's junction law follows from conservation of charge.
(B) Kirchhoff's loop law follows from conservative nature of electric field.
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Two metal plates having charges Q, −Q face each other at some separation and are dipped into an oil tank. If the oil is pumped out, the electric field between the plates will
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A dielectric slab is inserted between the plates of an isolated charged capacitor. Which of the following quantities will remain the same?
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A dielectric slab is inserted between the plates of a capacitor. The charge on the capacitor is Q and the magnitude of the induced charge on each surface of the dielectric is Q'.
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Find the circuit in the three resistors shown in the figure.

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