Optical Properties

The ionization potential (IP) is the energy required to remove an electron from the ground state of an atom. For a hydrogen atom, the ionization potential is given by: Correct Answer: The ionization potential of the electron in the ground state of a hydrogen atom is .

The focal length of a lens is determined by the refractive index difference between the material of the lens and the medium around it. When the lens is dipped in water, the refractive index of the medium increases, reducing the refractive index difference and causing the lens to behave more like a divergent lens.

Ampere's Circuital Law states that the magnetic field around a closed loop is proportional to the current passing through the loop. The law is expressed mathematically as: where:
- is the circulation of the magnetic field around the loop,
- is the permeability of free space,
- is the current enclosed by the loop.

Specific conductivity ( ) is related to the drift velocity ( ) by the equation: where:
- is the number density of charge carriers,
- is the charge of the carriers,
- is the cross-sectional area of the conductor.

The focal length of a lens in air is given by the lens formula: where is the refractive index of the material of the lens, and and are the radii of curvature of the lens. When the lens is immersed in a liquid of refractive index , the focal length is: The ratio of the focal lengths is:

The focal length of a lens is dependent on the wavelength of the light passing through it. For a convex lens, the focal length is greatest for red light, as it has the longest wavelength.

Step 1: Understanding the Concept:
Total Internal Reflection (TIR) is a special case of reflection that occurs under specific conditions at the boundary between two transparent media. It's the principle behind optical fibers.

Step 2: Detailed Explanation:
For TIR to occur, two necessary conditions must be met: \begin{enumerate} \item Medium of Travel: The light ray must be traveling from a medium with a higher refractive index (optically denser) to a medium with a lower refractive index (optically rarer). For example, from water to air, or from glass to water.
\item Angle of Incidence: The angle of incidence ( ) in the denser medium must be greater than a specific angle called the critical angle ( ). The critical angle is the specific angle of incidence for which the angle of refraction is 90 degrees.
\end{enumerate} When these two conditions are satisfied, no light is refracted into the rarer medium; instead, the entire ray is reflected back into the denser medium, following the laws of reflection (angle of incidence = angle of reflection).

Step 3: Final Answer:
Total internal reflection is an optical phenomenon in which a light ray traveling from an optically denser medium to an optically rarer medium is completely reflected back into the denser medium. This happens when the angle of incidence at the interface is greater than the critical angle for the pair of media.

Step 1: Understanding the Concept and Given Data:
We are dealing with an astronomical telescope where the object is at a finite distance, not at infinity. For "normal vision" or "normal adjustment", the final image must be formed at infinity. This means the intermediate image formed by the objective lens must be located at the principal focus of the eyepiece. \begin{itemize} \item Focal length of objective, cm. \item Focal length of eyepiece, cm. \item Object distance for objective, cm. \end{itemize}

Step 2: Find the position of the intermediate image ( ):
We use the lens formula for the objective lens: The objective lens forms a real, inverted image 50 cm away from it.

Step 3: Find the distance between the lenses ( ):
For the final image to be at infinity (normal vision), the intermediate image formed by the objective must be at the first focal point of the eyepiece. Thus, the distance of the intermediate image from the eyepiece is cm. The total distance between the objective and eyepiece lenses is the sum of their separation:

Step 4: Find the magnification ( ):
The angular magnification of a telescope is given by , where is the angle subtended by the final image at the eye and is the angle subtended by the object at the objective. where is the object height and is the height of the intermediate image. The linear magnification of the objective is . The overall image is inverted. Substituting the values: