NDA (II) 2016 General Ability Test · Question 112 of 150

Correct — D, between the pole of the mirror and the principal focus. A concave mirror is a converging mirror, and for every object position from infinity down to the focus it gathers the reflected rays to an actual crossing point, so the image is real and inverted. Only when the object comes closer than the focal length do the reflected rays diverge instead of converging; they can then be traced back to an apparent crossing point behind the mirror, giving an image that is virtual, erect and larger than the object. That is the single position on the whole list that produces all three of the properties the question names, and it is the position a shaving mirror or a dentist's mirror is used in.

• (a)at the principal focus — With the object exactly at the focus, the reflected rays come off parallel and never meet, so the image is formed at infinity. It is described as real, inverted and very highly magnified — not virtual and erect.
• (b)at the centre of curvature — This is the symmetric case: the image forms back at the centre of curvature itself, is real and inverted, and is exactly the same size as the object. Nothing about it is virtual, erect or magnified.
• (c)beyond the centre of curvature — Here the image falls between the focus and the centre of curvature and is real, inverted and diminished. This is the arrangement used when a concave mirror is made to project a small bright image, and it is the opposite of what the question describes.

For a spherical mirror the pole is the centre of the reflecting surface, the centre of curvature is the centre of the sphere it was cut from, and the principal focus lies halfway between them, so the focal length is half the radius of curvature. A concave mirror converges parallel light to its focus and can form either a real or a virtual image depending on where the object stands. A convex mirror always diverges the light, so its image is always virtual, erect and diminished, whatever the object distance.

Learning the six object positions for a concave mirror as a table is worth more marks than the mirror formula, because the exam usually asks for the description rather than the distance. Read the table from far to near and one pattern stands out: the image marches steadily outward from the focus as the object marches inward towards it, staying real and inverted the whole way, and then flips character completely the moment the object crosses the focus. The mirror formula 1/v + 1/u = 1/f says the same thing algebraically — inside the focal length the sign of v changes, and a negative image distance in the usual convention means the image is behind the mirror and therefore virtual.

• For a spherical mirror the focal length is half the radius of curvature, f = R/2.
• A concave mirror gives a virtual, erect and magnified image only when the object lies between the pole and the principal focus.
• With the object at the centre of curvature the image is real, inverted and the same size, formed at the centre of curvature itself.
• A convex mirror always gives a virtual, erect and diminished image, which is why it is used as a rear-view mirror for its wide field of view.

• Assuming a concave mirror always gives a real image; it does for every position except inside the focal length.
• Confusing 'at the focus' with 'inside the focus' — the first gives an image at infinity, the second the virtual erect image asked for here.
• Attaching the always-virtual property to the wrong mirror; it belongs to the convex mirror, not the concave one.

Spherical mirrors appear in the GAT most years, either as this description-to-position match or as a short numerical using the mirror formula, so keep the table and the formula both ready.

• practice — not a real PYQ

  An object is placed at the centre of curvature of a concave mirror. The image formed is

  • (a)virtual, erect and magnified
  • (b)real, inverted and of the same size
  • (c)real, inverted and diminished
  • (d)virtual, erect and diminished

  Answer(b) real, inverted and of the same size — and it is formed at the centre of curvature itself.

• practice — not a real PYQ

  A convex mirror of radius of curvature 40 cm has a focal length of

  • (a)10 cm
  • (b)20 cm
  • (c)40 cm
  • (d)80 cm

  Answer(b) 20 cm — for any spherical mirror the focal length is half the radius of curvature.