Sunday, 10 May 2020

REFLECTION AT CURVED SURFACES - CONCAVE AND CONVEX MIRRORS - A COMPLETE STUDY

SPHERICAL MIRRORS ----  CURVED SURFACES  - KEY CONCEPTS




Let us look at the below diagram, reflection at plane surfaces i.e. at plane mirror. All the laws of reflection at plane surfaces are valid and applicable to spherical mirrors also.

plane mirror reflection property



SPHERICAL MIRROR ?


The mirrors which have curved surface are known as Spherical mirrors, these mirrors are part of a hollow glass sphere.

CONVEX MIRROR AND ITS TERMS


The spherical mirror is said to be convex if the bulged surface is made smooth and the inner surface is silvered. 






CONCAVE MIRROR AND ITS TERMS 





The spherical mirror is said to be concave if the bulged surface is silvered and the inner surface is made smooth.




SPHERICAL MIRRORS AND TERMS RELATED :

APERTURE: The surface of the mirror from which the reflection take place is called its aperture.

POLE: The central point on the surface of the mirror is called its pole (P)

CENTRE OF CURVATURE:

The centre of the sphere of which the spherical mirror is a part is called the centre of curvature of the mirror.

RADIUS OF CURVATURE::

The radius of the sphere from which the spherical mirror is a part is called the radius of curvature of the mirror.

PRINCIPAL AXIS:

The line joining the pole and the centre of curvature is called the principal axis of the mirror.

FOCUS: (F)

The point on the principal axis where rays incident parallel to the principal axis converge to reappear or to diverge from after reflection is called the Focus of the spherical mirror.


FOCAL LENGTH (f):

The distance of the Focus from the pole is called the focal length (f) of the spherical mirror.

REAL AND VIRTUAL IMAGES:


An image formed by the actual intersection of light rays is called a real image. A real image is formed on the screen.

If the rays of light responsible for an image do not actually intersect, the image is called virtual image.

Virtual image cannot be formed on the screen, as no light reaches where the image appears to form.





Observe the following ray diagram when a parallel light incidents on a concave mirror and understand the reflection concepts........





 IMAGES FORMED BY A CONVEX MIRROR:

Irrespective of the position of the object , The image formed by the convex mirror is always virtual and erect but when we compare the the size of the image, the image size  is always diminished.  

PRINCIPAL FOCUS OF A CONVEX MIRROR
The principal focus of a convex mirror, which is divergent mirror,  is a point on the principal axis of the mirror, at which all the incident rays parallel to the principal axis appears to diverge after reflection from the mirror.


 The principal focus of the convex mirror is virtual and always lies behind the convex mirror. 


observe the above ray diagram when parallel rays incident on both concave mirror and convex mirror and observe the principal focus. 


from the above ray diagrams, write down the characteristics of the image formed.






MIRROR FORMULA:


1/v + 1/u = 1/f

From the mirror formula, if we observe, we can understand that how the object distance,u, and image distance,v, are related to the focal length.  The distances are measured from the pole only. Pole to object is u, and pole to image is v, 

MAGNIFICATION BY SPHERICAL MIRRORS:
Generally, we can understand that the magnification is the increase in the image size with respect to the size of the object which is produced by spherical mirrors.  The magnification is calculated by taking the ratio of height of the image to the height of the object ---- hi/ho.  It can also be calculated by the negative ratio of the image distance to the object distance.

 What can we understand from the magnification ?

*** when 'm' value is positive it tells us image is virtual.
*** when 'm' value is negative it tells us image is real.



logical question combining mirror formula and magnification


FIND OUT THE OBJECT DISTANCE (u), when the magnification produced is 'm' and focal length is 'f'.

solution:    

mirror formula is :  1/f = 1/v + 1/u



  magnification is m = -v/u   so  v=-mu

substituting the 'm' value in formula:

  1/f = 1/-mu   + 1/u

1/f = 1/u(1/-m + 1/u)

    simplifying,   u = f/m(m-1)

critical thinking problems:


1. Suppose that you are given a concave mirror of focal length 15 cm.  Then, 

a) To get the magnification m=1, where the object is needed to be placed
b)  When the object is placed at 30 cm, write the characteristics of the image formed.
c)  Your friend told that the image formed at infinity, where would be the object is placed.



2. When a student is performing experiment with concave mirror of focal length 20 cm, then he observed that the size of the image is reduced to 1/3rd of its size of the object.  Calculate the object distance in this situation. 






  

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