Ray Optics and Optical Instruments Test 11

u = f+x

Using mirror formula,

1/v+1/u = 1/f

Or, 1/v – 1/(f+x) = – 1/f

∴ v = – f(f+x)/x

Magnification (m) = size of image / size of object = – v/u

So, the assertion and reason both are true and the reason properly explains the assertion.

Air bubbles shine in water due to total internal reflection. Total internal reflection is a special case of refraction when light passes from denser medium (water) to rarer medium (air inside the bubble) and angle of incidence is more than the critical angle. So, the reason is also true. The reason also explains the assertion properly.

Speed of light is slower in glass compared to that in air. Hence the refractive index of glass is more than that of air. So the reason is true.

When a double convex air bubble is formed within a glass slab, the refractive index of the medium of the bubble is less than the refractive index of the surrounding medium. Hence the lens will not behave like a converging lens. It will behave like a diverging lens. So, the assertion is false.

For normal adjustment, a 30 cm lens final image cannot form image at the near point (25 cm from the eye). So the statement is true.

Convex lens behaves like a simple microscope. The assertion is true.

The magnifying power of a convex lens is expressed as:

• For least distance of distinct vision,

• For relaxed eye, m = D/f

Since f is in the denominator, for larger magnifying power, focal length should be small. So, the reason is also correct and it is the assertion.

Convex mirror always form virtual image. So, the assertion is true.

Parallel rays incident on convex mirror do not actually meet. They get reflected in such a manner that their extension meet at a point. So, the reason is false.

The mirror formula is derived under the consideration that the incident rays are paraxial which means that the rays lie very close to the principal axis. Hence the mirror aperture is considered to be small. So, the assertion is true.

Laws of reflection are valid for any surface plane or spherical. Hence the reason is false.

Refractive index of diamond with respect to the liquid is √6 / √3 = √2 So, the critical angle for the diamond-liquid pair of media is sin–1(1/ √2 ) = 45°.

For total internal reflection, angle of incidence should be greater that critical angle.

Since angle of incidence is 30°, total internal reflection cannot take place.

So, the assertion is false. But the reason is true.

When light is passed through a true solution does not occur. Scattering occurs when light is passed through a colloidal solution. So, the assertion is false.

In Rayleigh scattering intensity of scattered light is inversely proportional to the fourth power of wavelength, blue light is scattered much more strongly than red light. Hence the reason is true.

Magnification of microscope is inversely proportional to focal lengths of objective lens and the eyepiece lens. Hence both the focal lengths are small. On the other hand, magnification of microscope is inversely proportional to focal lengths of eyepiece lens and directly proportional to the objective lens. So, the focal length of the objective lens is large and the focal length of the eyepiece lens is small.

Hence, if the objective lens and the eyepiece lens of a microscope are interchanged that will not meet the criterion of the telescope.

So, the reason is true. But the assertion is false.