Summary of HC Verma Solutions Part 1 Chapter 22: Photometry
FAQs on HC Verma Solutions Class 11 Chapter 22 - Photometry
1. How do you solve problems in HC Verma Chapter 22 that involve comparing two light sources using a photometer?
To solve problems involving the comparison of two light sources, you apply the principle of photometry. This principle states that the illuminance (E) produced by the two sources on a screen is equal when the screen appears equally bright from both sides. The step-by-step method is as follows:
- Place the two light sources, S1 and S2, with luminous intensities I1 and I2 on the photometer bench.
- Adjust their distances, r1 and r2, from the screen until the illuminance from both is equal.
- Apply the formula for illuminance, which follows the inverse square law: E = I / r².
- Set the illuminances equal: E1 = E2, which gives I1 / r1² = I2 / r2².
- Using the measured distances r1 and r2, you can calculate the ratio of their luminous intensities or find an unknown intensity if one is given.
2. What are the key formulas from Chapter 22 - Photometry needed to solve numericals in HC Verma?
To successfully solve numericals from HC Verma's chapter on Photometry, you should be familiar with these fundamental formulas:
- Luminous Intensity (I): Measured in candela (cd). It is the fundamental quantity.
- Luminous Flux (Φ): The total light energy perceived by the eye per unit time. The formula relating it to intensity is Φ = I * ω, where ω is the solid angle in steradians. For a source emitting uniformly in all directions, the total flux is Φ = 4πI. Measured in lumens (lm).
- Illuminance or Illumination (E): The luminous flux incident per unit area. For a source at a distance 'r', the formula is E = Φ / A = I / r². It is measured in lux (lm/m²).
- Principle of Photometry: For two sources producing equal illuminance, I1 / r1² = I2 / r2².
3. Why is luminous flux measured in lumens instead of watts in photometry?
The distinction between lumens and watts is crucial. A watt is a unit of radiant flux, measuring the total power of electromagnetic radiation emitted by a source. However, the human eye is not equally sensitive to all wavelengths (colours) of light. Photometry specifically deals with light as perceived by a typical human eye. The lumen is a unit of luminous flux, which weights the radiant flux at each wavelength according to the eye's sensitivity curve. Therefore, two light sources with the same power in watts can have different luminous flux in lumens if one emits more light in the green-yellow region, where the eye is most sensitive.
4. What is the fundamental principle behind a Lummer-Brodhun photometer used in HC Verma exercises?
The fundamental principle of the Lummer-Brodhun photometer is to enable a precise comparison of illuminance from two different light sources. It uses a clever optical system, typically involving a pair of prisms, to project light from both sources onto two sides of a white, opaque screen. The observer looks through an eyepiece and sees a field of view composed of parts illuminated by each source. The distances of the sources are adjusted until the dividing lines between these parts disappear, indicating that the illuminance from both sources is identical. At this point, the I / r² relationship can be applied to compare their luminous intensities.
5. How does the inverse square law specifically apply to illuminance problems in photometry?
The inverse square law is central to solving photometry problems. It states that the illuminance (E) produced by a point source of light on a surface is inversely proportional to the square of the distance (r) of the surface from the source. The formula is E ∝ 1/r². This means if you double the distance from a light source, the illuminance on a surface drops to one-fourth of its original value. This principle is the basis for comparing luminous intensities, as seen in the photometer equation I1/r1² = I2/r2².
6. What are the most common mistakes students make when solving HC Verma problems on photometry?
When solving photometry problems from HC Verma, students should watch out for these common errors:
- Confusing Terms: Mixing up luminous intensity (I, in candela), luminous flux (Φ, in lumens), and illuminance (E, in lux). Each has a distinct definition and unit.
- Forgetting to Square: In the inverse square law (I/r²), a frequent mistake is using the distance 'r' instead of 'r²'.
- Unit Conversion Errors: Ensure all distances are in the same unit (e.g., meters) before applying the formula.
- Misunderstanding Solid Angle: When calculating total luminous flux (Φ = 4πI), students sometimes forget that this applies to a source radiating uniformly in all directions.
7. What is the relationship between luminous intensity, luminous flux, and illuminance as per Class 11 Physics?
These three quantities are fundamentally linked in photometry. Think of it this way:
- Luminous Intensity (I): This is the starting point. It describes how much light power is radiated from a point source in a specific direction. Its unit is the candela (cd).
- Luminous Flux (Φ): This is the total perceived light emitted by a source into a certain solid angle or in all directions. It is derived from intensity (Φ = I × solid angle). Its unit is the lumen (lm).
- Illuminance (E): This describes how much luminous flux lands on a specific surface area. It depends on both the source's intensity and the distance to the surface (E = I/r²). Its unit is lux (lm/m²).
