Which mirror always produces a virtual image of same size?

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Question

Virtual, upright and magnifiedReal, inverted and magnifiedReal, inverted and diminishedAll of the above

Convex mirror forms virtual image, diminished and upright image.

The correct answer is: All of the above

The convex mirror will not form a real image. Convex mirrors will not produce a magnified image of an object. Convex mirrors will always produce an upright image.  So, the correct option is d.

A beam of light converges at a point P. Now a lens is placed in the path of the convergent beam 12 cm from P. At what point does the beam converge if the lens is (a) a convex lens of a focal length 20 cm, and (b) a concave lens of focal length 16 cm?

Here, the point P on the right of the lens acts as a virtual object.

Object distance, u = 12 cm

∴           1v =120+112      =3+560 =860

i.e.,           v = 60/8 = 7.5 cm. 

Image is at a distance of 7.5 cm to the right of the lens, where the beam converges. (b)Now,Focal length of concave lens, f = –16 cmObject distance, u = 12 cm 

⇒      v = 48 cm 

Hence, the image is at a distance of 48 cm to the right of the lens, where the beam would converge.

Text Solution

Solution : From mirror formula <br> `(1)/(v)+(1)/(u)=(1)/(f) rArr(1)/(v)=(1)/(f)-(1)/(u)` <br> For convex mirror, <br> Object distance `u` is negative and the focal length `f` is positive. <br> `therefore (1)/(v)=(1)/(+f)-(1)/(-u)=(1)/(f)+(1)/(u)` <br> Therefore, the image distance is always positive incase of a convesx mirror. <br> Hence, the convex mirror always formed a virtual image.