Physics Lab Experiments: Optics and Circuits
Physics Laboratory Procedures and Principles
Experiment 1: Focal Length of a Convex Lens Using a Graph
AIM: To find the focal length of a convex lens using a graph.
PRINCIPLE: For an object placed at a distance $u$ from the pole of a lens with focal length $f$, the image is formed at a distance $v$ from the pole. The relation between these distances is given by the lens formula: $\frac{1}{f} = \frac{1}{v} – \frac{1}{u}$ (or $\frac{uv}{u+v}$ if rearranged for $f$).
Experiment 2: Resistance Per Unit Length of a Wire
AIM: To determine the resistance per unit length of a given wire by plotting a graph of $V$ versus $I$.
PRINCIPLE: Ohm’s Law: The current flowing through a conductor is directly proportional to the potential difference across its ends, provided all physical conditions remain the same. Mathematically, $V = IR$, so $R = \frac{V}{I}$. The resistance per unit length is the slope of the $R-L$ graph, or derived from the resistance $R$ and the wire’s length $L$.
Experiment 3: Focal Length of a Concave Lens
AIM: To find the focal length of a concave lens using a convex lens.
PRINCIPLE: A concave lens forms a virtual image. When a concave lens of higher focal length is introduced between the convex lens and its real image position, the image is shifted farther away. The concave lens forms a real image of the object (which is the image formed by the convex lens alone). The lens formula used is $\frac{1}{f_{\text{concave}}} = \frac{1}{v} – \frac{1}{u}$, where $u$ and $v$ are determined based on the setup.
Experiment 4: Combination of Resistances Using a Meter Bridge
AIM: To verify the law of combination of resistances (series/parallel) using a meter bridge.
PRINCIPLE: The meter bridge works on the principle of a balanced Wheatstone bridge. If $P$ is the unknown resistance in the left gap and $Q$ is the known resistance in the right gap, and $L$ is the balancing length from the left end, then: $P = Q \frac{L}{100 – L}$.
Experiment 5: Galvanometer Resistance and Figure of Merit
AIM: To determine the resistance of a galvanometer by the half-deflection method and to find its figure of merit.
PRINCIPLE:
- (a) Resistance of Galvanometer ($G$): Let $S$ be the resistance in series with the galvanometer. When a known current flows, let the deflection be $\theta_1$. When $S$ is shunted by a resistance $R$ such that the deflection becomes $\theta_1/2$, the resistance $G$ can be calculated using the relationship derived from current division: $G = \frac{RS}{R-S}$ (assuming specific circuit configurations for deflection measurement).
- (b) Figure of Merit ($K$): It is defined as the current required to produce a deflection of one division in the scale of the galvanometer. $K = \frac{\text{Current}}{\text{Deflection}}$. In terms of EMF and circuit components: $K = \frac{\epsilon}{(R+G) \theta}$, where $\theta$ is the deflection in divisions.
Experiment 6: Resistance and Resistivity Using a Meter Bridge
AIM: To determine the resistance of a given wire using a meter bridge and hence to determine the resistivity ($\rho$) of the material of the wire.
PRINCIPLE: The meter bridge works on the principle of a balanced Wheatstone’s bridge. When the galvanometer shows no deflection for a particular position $L$ of the jockey $J$ on the wire, the bridge is balanced. The unknown resistance $P$ is found using $P = Q \frac{L}{100-L}$. The resistivity $\rho$ is then calculated using $\rho = \frac{\pi r^2 P}{L_{\text{wire}}}$, where $r$ is the radius and $L_{\text{wire}}$ is the length of the wire.
Experiment 7: Focal Length of a Concave Mirror
AIM: To find the value of $v$ for different values of $u$ in the case of a concave mirror and to find the focal length ($f$).
PRINCIPLE: The relationship between object distance ($u$), image distance ($v$), and focal length ($f$) for a spherical mirror is given by the mirror formula: $\frac{1}{f} = \frac{1}{u} + \frac{1}{v}$. Rearranging for $f$: $f = \frac{uv}{u+v}$.
Experiment 8: Converting Galvanometer to Voltmeter
AIM: To convert the given galvanometer into a voltmeter of a desired range and to verify the same.
PRINCIPLE: A galvanometer of resistance $G$ is converted into a voltmeter of range $0-V$ by connecting a suitable high resistance $R$ in series with the galvanometer. The required series resistance $R$ is calculated using the maximum current the galvanometer can handle ($I_g$): $R = \left(\frac{V}{I_g}\right) – G$.
Experiment 9: V-I Characteristic of a PN Junction (Forward Bias)
AIM: To draw the $V-I$ characteristic curve of a PN junction in Forward bias.
PRINCIPLE: When the $P$-side of the semiconductor is connected to the positive terminal and the $N$-side to the negative terminal of the external source, the diode is in forward bias. As the forward voltage increases, the current increases slowly until the cut-in voltage (or knee voltage) is reached, after which the current increases rapidly.
Experiment 10: Internal Resistance of a Primary Cell
AIM: To determine the internal resistance ($r$) of a given primary cell using a potentiometer.
PRINCIPLE:
- When the key $K_2$ (shunting the cell) is open, let the balancing length be $L_1$. The potential difference across the cell is equal to its EMF ($\epsilon$): $\epsilon \propto L_1$.
- When $K_2$ is closed, let the balancing length be $L_2$. The potential difference ($V$) across the cell terminals is $V \propto L_2$.
- The internal resistance $r$ is calculated using the formula: $r = R \left(\frac{L_1 – L_2}{L_2}\right)$, where $R$ is the resistance in the rheostat box.
Experiment 11: Zener Diode Characteristics
AIM: To draw the characteristic curve of a Zener diode and determine its reverse breakdown voltage.
PRINCIPLE: A Zener diode is a semiconductor diode where the $P$ and $N$ regions are heavily doped, resulting in a low and specific reverse breakdown voltage ($V_Z$). When reverse biased, initially, only a small leakage current flows due to minority charge carriers. Upon reaching $V_Z$, the current increases sharply due to Zener breakdown.
Experiment 12: Comparing EMFs of Two Cells
AIM: To compare the EMF of two given primary cells using a potentiometer.
PRINCIPLE: The balancing length obtained on the potentiometer wire is directly proportional to the EMF of the cell used. Let $AJ_1 = L_1$ be the balancing length for the cell of EMF $\epsilon_1$, and $AJ_2 = L_2$ for the cell of EMF $\epsilon_2$. If $\Phi$ is the potential drop per unit length of the wire, then $\epsilon_1 = \Phi L_1$ and $\epsilon_2 = \Phi L_2$. Therefore, the ratio is: $\frac{\epsilon_1}{\epsilon_2} = \frac{L_1}{L_2}$.
Experiment 13: Frequency of AC Mains
AIM: To find the frequency of the AC mains supply using a sonometer or similar apparatus.
PRINCIPLE: If $V$ is the frequency of the AC supply, the electromagnet connected to the supply magnetizes and demagnetizes $2V$ times per second. Consequently, the sonometer wire between the two bridges is attracted and released $2V$ times per second, causing vibrations at twice the supply frequency.