Lab Quiz Relationships and Conditions

phy-1109 PHY-1109 Physics

Summary of Experimental Relationships

Experiment	Quantity (X)	Relationship to Quantity (Y)	Condition/Equation
E12: Spectrometer (Prism)	Deviation	$\propto$ Wavelength ($\lambda$)	Deviation increases with shorter wavelengths (e.g., greater for violet than red).
	Deviation	$\propto$ Angle of Incidence	Deviation is minimum at a specific angle of incidence, and increases otherwise.
	Minimum Deviation (${\delta }_m$)	$\propto$ Color	White light gives a different ${\delta }_m$ value for different wavelengths; Sodium light gives a single value.
E18: Potentiometer	E.M.F. ($E_1$)	$\propto$ Balancing Length ($l_1$)	$E_1=\rho l_1$ (where $\rho$ is the potential drop per unit length).
	Sensitiveness	$\propto$ Balancing Length	Sensitiveness increases as balancing length increases.
	Null Point	Independent of High Resistance	High resistance in series with the galvanometer does not interfere with the null point.
	Null Point	Independent of Driver Cell Change	Potential distribution hangs equally, maintaining the null point constant even if driver cell E.M.F. changes.
E13: Newton’s Rings	Center Appearance	$\propto$ Interference/Phase Shift	Center is dark in reflected light due to destructive interference ($\pi$ phase change).
	Fringes	$\propto$ Light Type	Monochromatic light (Sodium light) is required; white light causes fringes to overlap.
E6: Specific Heat (Cooling)	Rate of Heat Loss ($\frac{dQ}{dt}$)	$\propto$ Temperature Difference ($\theta -{\theta }_0$)	$\frac{dQ}{dt}\propto (\theta -{\theta }_0)$ (Newton’s Law of Cooling). (Strictly true only for small $\theta$ differences, preferably $\le 30^{\circ }\text{C}$).
	Radiation Loss	$\propto$ Surface Area	Using the same volume of liquids keeps the surface area for radiation equal.
	Thermal Law Validity	$\propto$ Material State	Newton’s law of cooling holds only for liquids, not for solids.
E20: Photoelectric Effect	Electric Current	$\propto$ Light Intensity	The number of electrons ejected (current) is proportional to the intensity.
	Electric Current	Independent of Frequency ($\nu$)	The current is independent of the frequency of incident radiation (above the threshold ${\nu }_0$).
	Photoemission	$\propto$ Frequency ($\nu$)	Emission occurs only when $\nu$ is greater than or equal to the threshold frequency (${\nu }_0$).
	Photon Energy	$\propto$ Frequency	Shorter waves (higher $\nu$, e.g., blue light) have higher energies than red light.
E14/E15: Diffraction Grating	Principle Maximum	Equation	$(a+b)\sin \theta =n\lambda$.
	Angle of Diffraction ($\theta$)	$\propto$ Wavelength ($\lambda$)	$\theta$ is proportional to $\lambda$ (when $\theta$ is not very large).
	Order ($n$)	$\propto$ Grating Element ($a+b$)	The $n^{th}$ order is absent if $(a+b)<n\lambda$.
	Order Separation	$\propto$ Number of Rulings ($N$)	If $N$ increases, order separation is large. If $N$ decreases, order separation is small.
E17: Post Office Box	Balance Condition (Wheatstone)	Equation	$S/R=Q/P$.
	Resistance ($R$)	$\propto$ Temperature ($t$)	Resistance increases with temperature. $R_t=R_0(1+\alpha t+\beta t^2)$.
	Bridge Sensitivity	$\propto 1/$ Resistance	Sensitivity is greater when the resistance of the galvanometer and battery are lower.
E7: Thermal Conductivity	Thermal Conductivity ($K$)	$\propto 1/$ Temperature	$K$ decreases with a rise of temperature.
	Thermal Conductivity ($K$)	Independent of Dimension	$K$ depends only on the material, not the dimension.
E8: Melde’s Experiment	Tension ($T$)	$\propto$ Arrangement Type	Tension in the longitudinal arrangement is one-fourth of that in the transverse arrangement.

In Experiment E17 (P.O. Box), how does the sensitivity of the Wheatstone bridge depend on the components used, and why is this relationship important?