Image Formation By Spherical Mirrors - Practice Questions & MCQ

Image formation by spherical mirrors

Sign conventions : 

• In the cartesian sign convention direction of the incident, the ray is taken as +ve.
• All the measurements are measured from the pole.
• If the incident ray is travelling from left to right the distance, measurement along the right direction will be taken as positive. 
• We can treat this direction as +ve x-axis direction and rest can be decided on the basis of graph that we use in mathematics.  Like upward direction will be taken as +ve as it is +ve y-axis. And downward as -ve
• Height above the principle axis is taken as positive and below it are taken as negative.
• Angles measured from the normal in anti-clockwise sense are positive, while that in clockwise senses are negative.

Rules for ray diagrams:

 The position of the image formed by spherical mirrors can be found by taking two rays of light coming from a point on the object which intersects each other to form an image. The following are the rules which are used for obtaining images formed by spherical mirrors.

 (1). A ray of light that runs parallel to the principal axis, after reflection, passes through the principal focus F of a concave mirror or appears to pass through the principal focus of a convex mirror.

 

(2). A ray of light passing through the center of curvature in a concave mirror or a ray of light going towards the center of curvature of a convex mirror is reflected back along the same path.

 

(3). A ray of light passing through the principal focus of a concave mirror or appearing to pass through the principal focus of a convex mirror becomes parallel to the principal axis after reflection.

 

 (4).  A ray incident at pole is reflected back making same angle with principle axis.

Image formation by concave mirror:

1. For a real object very far away from the mirror, the real image is formed at the focus.

  

2. For a real object close to the mirror but outside of the center of curvature, the real image is formed between C and f. The image is inverted and smaller than the object.

  

3. For a real object at C, the real image is formed at C. The image is inverted and the same size as the object. 

4.  For a real object between C and f, a real image is formed outside of C. The image is inverted and larger than the object. 

5.  For a real object at f, no image is formed. The reflected rays are parallel and never converge. 

6. For a real object between f and the mirror, a virtual image is formed behind the mirror. The position of the image is found by tracing the reflected rays back behind the mirror to where they meet. The image is upright and larger than the object. 

  

Image formation by convex mirror: 

1. When the object is at the infinity, a point sized image is formed at principal focus behind the convex mirror. 

Properties of image: Image is highly diminished, virtual and erect.

2.  When the object is between infinity and pole of a convex mirror, a diminished, virtual and erect image is formed between pole and focus behind the mirror. 

Properties of image: Image is diminished, virtual and erect.