An object of size 70 mm is place at 27 cm in front of a concave mirror of focal length 18 cm . At what distance from the mirror should a screen be placed so that a sharp focussed image can be obtained? Find the size and nature of the image.

Height of the object h 1 = 70 mm = 7 cm Object distance u = - 27 cm The focal length of a concave lens f = - 18 cm Let the image distance be found be v . According to the mirror formula, 1 f = 1 v + 1 u ∴ 1 v = 1 f - 1 u ∴ 1 v = 1 - 18 - 1 - 27 ∴ 1 v = 9 - 18 × 27 v = - 54 cm The screen should be placed 54 cm to the left of the pole to get a sharp image. Let the height of the image be found be h 2 . Magnification M is given by, M = - v u = h 2 h 1 ∴ - - 54 - 27 = h 2 7 ∴ h 2 = - 14 cm The height of the image is - 14 cm . As the image height and image distance are negative, The image is real, inverted, and enlarged.

Draw the ray diagram when an object is placed at twice the focal length of a Convex Lens.

Image formation by a lens depends on the wave property called refraction. It can be defined as the bending of waves when they enter a medium where their speed is different. In case when an object is placed at twice the focal length of a convex lens then a ray of light which is parallel to the principal axis after refraction pass through the focus F along with the direction, while the other ray passes through the optical centre and goes straight without any deviation. So these two refracted light rays intersect each other at a point on the other side of the lens at the centre of curvature 2F and the image formed in this case is at the centre of curvature will be of the same size as the object, real and inverted.