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SMA Physics • Physics Lab Class XII • Exp 17

🪞 Focal Length of Convex Mirror (using Convex Lens)

📖 Manual
📐 Optical Bench: Auxiliary Lens & Convex Mirror Setup
💡
Experiment Protocol: Auxiliary lens $L$ creates convergent rays towards focus $I$. Adjust the Convex Mirror Position ($x_M$) until rays fall normally on its surface and retrace their paths, forming an inverted image coinciding exactly with the Object Needle ($O$) with zero parallax!
Lens Position $x_L$:40.0 cm
Image Position $x_I$ (Lens alone):75.0 cm
Mirror Position $x_M$:51.0 cm
Radius of Curvature $R = x_I - x_M$:24.0 cm
🎛️ Bench Upright Positions Target $f \approx 12.0\text{ cm}$
Convex Mirror Position ($x_M$) 51.0 cm
Position between Lens ($40\text{cm}$) and Image ($75\text{cm}$) Move to remove parallax at O
Object Needle Position ($x_O$) 10.0 cm
Distance to Lens $u_L = x_L - x_O$ $u_L = 30.0\text{ cm}$
Observer Eye Transverse Shift (Parallax Test at O) Center
← Left Tilt Direct Center Right Tilt →
📐 Computed Optical Parameters
Radius of Curvature ($R = MI$)
24.0 cm
Focal Length ($f = R / 2$)
12.0 cm
Parallax Discrepancy
0.0 mm ✓
Light Path Status
Normal Reflection

Observation Table: Focal Length of Convex Mirror

Using Auxiliary Convex Lens. Formula: $R = x_I - x_M$, $f = R/2$.

S.No. Object Needle $x_O$ (cm) Lens $x_L$ (cm) Image without Mirror $x_I$ (cm) Mirror Position $x_M$ (cm) Radius of Curvature $R = x_I - x_M$ (cm) Focal Length $f = R/2$ (cm)
📊 Experimental Mean Result
Mean Radius of Curvature ($R$)
-- cm
Mean Focal Length ($f$)
-- cm

🎯 Aim of the Experiment

To find the focal length of a convex mirror, using an auxiliary convex lens.

📐 Governing Principle (Principle of Reversibility)

A convex mirror forms a virtual, diminished image behind its surface for any real object; hence its focal length cannot be measured directly using a real image on a screen.

An auxiliary convex lens forms a convergent beam of light that would meet at point $I$. When a convex mirror is placed in the path of these converging rays such that they strike the mirror normally, each ray retraces its path according to the principle of reversibility of light.

$$R = x_I - x_M \implies f = \frac{R}{2} = \frac{x_I - x_M}{2}$$

A real inverted image is then formed at the position of the object needle $O$. When parallax between the inverted image and the tip of the object needle is completely removed, point $I$ is exactly at the center of curvature $C$ of the mirror.

❓ Interactive Viva Voce Preparation