Draw a ray diagram to show refraction of a ray of monochromatic light passing through a glass prism.
Deduce the expression for the refractive index of glass in terms of angle of prism and angle of minimum deviation.
Explain briefly how the phenomenon of total internal reflection is used in fibre optics.
CBSE DELHI - SET 1 2011
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From $\Delta$ MQR, $(i - r_1) + (e - r_2)= \delta$
So$ (i + e)-(r_1 + r_2)= \delta$
From $\Delta PQN r_1+ r_2+ \angle QNR =180^\circ$
Also $A + \angle QNR =180^\circ$
Thus $A= r_1+ r_2$
So $ i + e - A= \delta$
At minimum deviation, $i = e, r_1= r_2 = r$ and $\delta = \delta_{m}$
$\Rightarrow \text{i} = \frac{\text{A} + \delta_{m}}{2}$
and $\text{r} = \frac{\text{A}}{2}$
Also $\mu = \frac{\sin\text{i}}{\sin\text{r}}$
Hence $\mu = \frac{\sin\bigg(\frac{\text{A} + \delta_{m}}{2}\bigg)}{\sin\bigg(\frac{\text{A}}{2}\bigg)}$
Each optical fibre consists of a core and cladding. Refractive index of the material of the core is higher than that of cladding. When a signal, in the form of light, is directed into the optical fibre, at an angle greater than the (relevant) critical angle, it undergoes repeated total internal reflections along the length of the fibre and comes out of it at the other end with almost negligible lossof intensity.
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Draw a labelled ray diagram to show the formation of image in an astronomical telescope for a distant object.
Write three distinct advantages of a reflecting type telescope over a refracting type telescope.
A convex lens of focal length 10 cm is placed coaxially 5 cm away from a concave lens of focal length 10 cm. If an object is placed 30 cm in front of the convex lens, find the position of the final image formed by the combined system.
With the help of a suitable ray diagram, derive the mirror formula for a concave mirror.
The near point of a hypermetropic person is 50 cm from the eye. What is the power of the lens required to enable the person to read clearly a book held at 25 cm from the eye?
Derive the lens formula, $\frac{1}{\text{f}} = \frac{1}{\text{v}} - \frac{1}{\text{u}}$ for a concave lens, using the necessary ray diagram.
Two lenses of powers 10 D and – 5 D are placed in contact.
Calculate the power of the new lens.
Where should an object be held from the lens, so as to obtain a virtual image of magnification 2?
A 4.5 cm needle is placed 12 cm away from a convex mirror of focal length 15 cm. Give the location of the image and the magnification. Describe what happens as the needle is moved farther from the mirror.
equiconvex lens (of refractive index 1.50) in contact with a liquid layer on top of a plane mirror. A small needle with its tip on the principal axis is moved along the axis until its inverted image is found at the position of the needle. The distance of the needle from the lens is measured to be 45.0 cm. The liquid is removed and the experiment is repeated. The new distance is measured to be 30.0 cm. What is the refractive index of the liquid?
With the help of a ray diagram, show the formation of image of a point object due to refraction of light at a spherical surface separating two media of refractive indices $n_1$ and $n_2 (n_2 > n_1)$ respectively. Using this diagram, derive the relation.
$\frac{\text{n}_2}{\text{v}}-\frac{\text{n}_1}{\text{u}}=\frac{\text{n}_1-\text{n}_2}{\text{R}}$
Write the sign conventions used. What happens to the focal length of convex lens when it is immersed in water?
A small block of mass m and a concave mirror of radius R fitted with a stand lie on a smooth horizontal table with a separation d between them. The mirror together with its stand has a mass m. The block is pushed at t = 0 towards the mirror so that it starts moving towards the mirror at a constant speed V and collides with it. The collision is perfectly elastic. Find the velocity of the image:
A Cassegrain telescope uses two mirrors. Such a telescope is built with the mirrors 20 mm apart. If the radius of curvature of the large mirror is 220 mm and the small mirror is 140 mm, where will the final image of an object at infinity be?