Worksheet
Worksheet • Class 12 Physics (Ray Optics)
Formula Box (use Cartesian sign convention)
- Mirror formula: \(\dfrac{1}{f} = \dfrac{1}{v} + \dfrac{1}{u}\)
- Magnification: \(m = -\dfrac{v}{u} = \dfrac{h_i}{h_o}\)
- Radius–Focal relation: \(R = 2f\) (applies to both concave & convex mirrors; sign from convention)
- Sign tips: For a concave mirror, \(f<0\). For a convex mirror, \(f>0\).
Drawing Hints (principal rays)
- Ray parallel to principal axis → passes through F (concave) / appears from F (convex).
- Ray through F → emerges parallel to axis.
- Ray through C (centre of curvature) → retraces its path.
Define the following key terms (1 mark each): (i) Pole (P) of a spherical mirror, (ii) Centre of curvature (C).
State the relation between radius of curvature R and focal length f. A concave mirror has R = 60 cm. Using the sign convention, find f with sign.
A convex mirror has R = 40 cm. Calculate its focal length and state its sign.
Using a neat ray diagram, show image formation by a concave mirror when the object is placed beyond C. State the nature and approximate position of the image.
Draw the ray diagram for a concave mirror with the object at the principal focus F. What is the nature and location of the image?
For a concave mirror, draw the ray diagram when the object is placed between F and P. State the nature, orientation, and relative size of the image.
Using a ray diagram, show image formation in a convex mirror for an object placed in front of it. Mention the nature and typical location of the image.
Numerical (concave): A concave mirror has f = −15 cm. An object is placed at u = −30 cm. Find the image distance v and magnification m.
Numerical (concave): A real image is formed at v = −24 cm when the object is at u = −36 cm. Determine the focal length f of the mirror (with sign).
Numerical (convex): For a convex mirror, f = +20 cm and the object is at u = −40 cm. Find the image distance v and magnification m.
Numerical (convex): A convex mirror produces an image that is half the size of the object. If the object is at u = −30 cm, find v and the focal length f.
Numerical (concave): A concave mirror forms a real image that is 3 times the size of the object. If f = −10 cm, at what distance u from the mirror should the object be placed?
Note: Use the given sign convention consistently. Show essential steps for numerical answers. Diagrams must be labeled (P, C, F, principal axis).