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The angle of incidence for a ray of light at a refracting surface of a prism is 45°. The angle of prism is 60°. If the ray suffers minimum deviation through the prism, the angle of deviation and refracting index of the material of the prism respectively are
In an astronomical telescope in normal adjustment a straight black line of length L is drawn on inside part of the objective lens. The eye-piece forms a real image of this line. The length of this image is l. The magnification of the telescope is:
In an astronomical telescope, the magnification is given by the ratio of the angle subtended by the image at the eye to the angle subtended by the object at the objective lens. This is equal to the ratio of the focal length of the objective lens to the focal length of the eyepiece. Therefore, the magnification is simply the ratio of the length of the object (L) to the length of the image (l).
If the focal length of the objective lens is increased, then magnifying power of :
The magnifying power of the microscope will decrease but the magnifying power telescope will increase.
The angle of a prism is A. One of its refracting surfaces is silvered. Light rays falling at an angle of incidence 2A on the first surface returns back through the same path after suffering reflection at the silvered surface. The refractive index μ of the prism is
When a light ray falls on a prism at an angle A and gets reflected from the silvered surface, the angle of incidence is 2A. For this to happen, the refractive index of the prism should be 2cosA, according to Snell's law.
A plane-convex lens fits exactly into a plano-concave lens. Their plane surfaces are parallel to each other. If lenses are made of different materials of refractive indices in μ1 and μ2 and R is the radius of curvature of the curved surface of the lenses. then the focal length of the combination is
(c) Focal length of the combination
1/f=1/f1+1/f2 ...(i)
We have f1=R/(μ1-1) and f2=R/(μ2-1)
or 1/f1=R/(μ1-1) or 1/f2=-R/(μ2-1)
Putting these values in Eq. (i), we get
1/f=(μ1-1)/R-(μ2-1)/R
=[μ1-1-μ2+1)/R]=(μ1-μ2/R)
For a normal eye, the cornea of eye provides a converging power of 40 D and the least converging power of the eye lens behind the cornea is 20 D. Using this information, the distance between the retina and the cornea-eye lens can be estimated to be
(c)
When a biconvex lens of glass having refractive index 1.47 is dipped in a liquid, it acts as a plane sheet of glass. This implies that the liquid must have refractive index
If biconvex lens behave like plane sheet, ray will pass undeviated through it only when medium has same refractive index as that of biconvex lens.
A concave mirror of focal length is placed at a distance of d from a convex lens of focal length A beam of light coming from infinity and falling on this convex lens concave mirror combination returns to infinity. The distance d must be equal
The magnifying power of a telescope is 9. When it is adjusted for parallel rays the distance between the objective and eyepiece is 20cm. The focal length of lenses are
Given,
So,
For the angle of minimum deviation of a prism to be equal to its refracting angle, the prism must be made of a material whose refractive index
For the angle of minimum deviation to be equal to the refracting angle of the prism, the refractive index of the prism material should lie between 2 and √2, according to the relation between the refractive index and the angle of minimum deviation.
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