Determination of the focal length of Concave mirror by obtaining the image of a distant object

Aim

To determine the focal length of a concave mirror by obtaining the image of a distant object.

Apparatus Required

  • Concave mirror
  • A meter scale
  • A screen
  • A mirror holder
  • A screen holder

Theory

  • A concave mirror is defined as the spherical mirror whose reflecting surface is curved inwards and follows laws of reflection of light.
  • When the object is at infinity, then real, inverted and highly diminished image is formed at focus.
  • The light rays coming from a distant object can be considered to be parallel to each other.
  • If the image formed is real, inverted and very small in size, then the parallel rays of light meet the point in the front of the mirror.
Fig 1:- Incident parallel rays are parallel to principal axis
Fig 2:- Incident parallel rays are not parallel to principal axis

Procedure

  1. Fix a concave mirror in the mirror holder and place it on the table near an open window. Turn the face of mirror towards a distant object (suppose a tree).
  2. Place the screen, fitted to a stand, in front of the concave mirror.
  3. Adjust the distance of screen, so that the image of the distant object is formed on it as given in the figure below. We can infer from the figure that a clear and bright image could be obtained if the distant object (a tree), is illuminated with sunlight and the screen is placed in the shade. A bright image of the Sun could also be obtained, if the sunlight is made to fall directly on the concave mirror.
  4. When a sharp image of distant object is obtained, then mark the position of the Centre of the stand holding the mirror and the screen as (a) and (b), respectively (see Fig 3).
  5. Measure the horizontal distance between the Centre of the concave mirror and the screen with the help of a measuring scale.
  6. Record the observations in the observation table.
  7. Repeat the experiment two more times by obtaining the images of two different distant objects and measure the distance between the concave mirror and the screen in each case. Record them in the observation table.
  8. Find the mean value of the focal length for all the observations for different objects.
Fig 3:- Determination of focal length of concave mirror

Observations

S. No.Name of the objectDistance between mirror and screen
(Focal length)
1.Polef1 = 29.8 cm
2.Tree 1f2 = 30 cm
3.Tree 2f3 = 30 cm

Calculation

Mean focal length = \inline \frac{f_{1} + f_{2} + f_{3}}{3} = \inline \frac{29.8 + 30 + 30}{3} = 29.93 cm

Result

The approximate value of focal length of the given concave mirror = 29.93 cm.

Precautions

  1. Concave mirror should be placed near an open window through which sufficient sunlight enters, with its polished surface facing the distant object.
  2. There should not be any obstacle in the path of rays of light incident on the concave mirror.
  3. In order to obtain a sharp and clear image of the distant object on the wall/ground, it must be ensured that the object is well illuminated, so that amount of light incident on the concave mirror is sufficient to produce a well illuminated and distinct image.
  4. The measuring scale should be parallel to the base of both the stands.
  5. The mirror holder along with the mirror should be kept perpendicular to the measuring scale for precise measurements.
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