The refractive index of diamond is 2.42. What is the meaning of this statement?

Refractive index of diamond is 2.42 implies that the ratio of the speed of light in air to that in the medium diamond is 2.42. 
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Define 1 dioptre of power of a lens.


One dioptre is defined as the power of a lens whose focal length is 1 metre. 
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A convex lens forms a real and inverted image of a needle at a distance of 50 cm from it. Where is the needle placed in front of the convex lens if the image is equal to the size of the object? Also, find the power of the lens.

Given, a convex lens.
Image distance, v = + 50 cm [v is positive for real image] 

As the real image is of the same size as that of the object, so

magnification, m= h'h = vu = -1 

 Object distance, u = -v = -50 cm. 

Now,  using th lens formula,

                       1f =1v-1u 
we have, 
                       1f= 1+50-1-50 1f= +250    f = +125

                     f = 25 cm = 0.25 m 

Power of the convex lens, P = 1f= 1+0.25 m = + 4 D. 

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Find the power of a concave lens of focal length 2 m.

Focal length of a concave lens is negative, so

                         f = - 2 m 
Therefore, 
Power, P = 1f(in m) = 1-2 m = -0.5 D. 
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We wish to obtain an erect image of an object, using a concave mirror of focal length 15 cm. What should be the range of distance of the object from the mirror? What is the nature of the image? Is the image larger or smaller than the object? Draw a ray diagram to show the image formation in this case.

The object should be placed between the focus F and the pole P of the concave mirror, i.e., between 0 and 15 cm from the mirror. Then the image will be virtual, erect and larger than the object. 

The object should be placed between the focus F and the pole P of the
Fig. Image formed by a concave mirror with the object between F and P

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