ā† Hub
SMA Physics ā€¢ Physics Lab Class XII ā€¢ Exp 19

šŸ” Focal Length of Concave Lens (Auxiliary Convex Lens)

šŸ“– Manual
šŸ“ Optical Bench: Auxiliary Convex Lens & Concave Lens Combination
šŸ’”
Experiment Step: In Stage 1, convex lens $L_1$ forms image $I_1$ at $60\text{ cm}$. In Stage 2, concave lens $L_2$ is placed between $L_1$ and $I_1$. Adjust the image needle to coincide with the shifted divergent image $I_2$ (zero parallax).
Concave Lens Pos $L_2$:48.0 cm
Virtual Obj Dist $u = I_1 - L_2$:12.0 cm
Image Needle Pos $I_2$:72.0 cm
Real Image Dist $v = I_2 - L_2$:24.0 cm
Parallax Status:ZERO PARALLAX āœ“
āš™ļø Optical Controls & Focal Length Calculation
1. Bench Upright Positions Bench 0 to 100 cm
Concave Lens Upright $L_2$: 48.0 cm
Image Needle Upright $I_2$: 72.0 cm
Observer Eye Lateral Shift: Center
šŸ“Š Concave Lens Results
Virtual Object $u$ ($I_1 - L_2$)
+12.00 cm
Real Image $v$ ($I_2 - L_2$)
+24.00 cm
Focal Length $f = \frac{u \cdot v}{u - v}$
-24.00 cm

šŸ“‹ Observation Table: Focal Length of Concave Lens

Obs # $L_1$ Pos (cm) $I_1$ Pos (cm) $L_2$ Pos (cm) $I_2$ Pos (cm) $u = I_1 - L_2$ (cm) $v = I_2 - L_2$ (cm) $f = \frac{uv}{u-v}$ (cm) Parallax Check
No observations logged yet. Adjust needles and click "Record to Observation Table".
šŸ“ˆ Experimental Mean Result
Mean Focal Length $f$: -- cm
Lens Power $P = 100/f$: -- D
šŸŽÆ Aim of the Experiment

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

šŸ“ Working Formula & Sign Convention
$$\frac{1}{f} = \frac{1}{v} - \frac{1}{u} \implies f = \frac{u \cdot v}{u - v}$$

Here, $I_1$ serves as a virtual object for the concave lens $L_2$. Since $I_1$ lies to the right of $L_2$, $u$ is positive (+). The diverging rays from $L_2$ form a real image at $I_2$, which also lies to the right of $L_2$, hence $v$ is positive (+). Since $v > u$, the denominator $(u - v) < 0$, yielding a negative focal length $f < 0$.

šŸ”¬ Step-by-Step Procedure
  1. Mount the auxiliary convex lens $L_1$ and object needle $O$ on an optical bench.
  2. Locate the real inverted image $I_1$ by moving an image needle until parallax is removed. Note the position of $I_1$.
  3. Place the given concave lens $L_2$ between $L_1$ and $I_1$. The image shifts farther away to $I_2$ due to divergence.
  4. Move the image needle to the new position $I_2$ and remove parallax between the needle and the image.
  5. Measure $u = I_1 - L_2$ and $v = I_2 - L_2$. Calculate $f = \frac{u \cdot v}{u - v}$. Repeat for 3-5 different positions of $L_2$.
ā“ Viva Voce Interactive Quiz