In the following experiment, we want to measure the slit width of our telescope using the spectral lines of an Hg-lamp. We place a grating and a prism between the lamp and the slit and determine the angular difference of the Hg lines. From the values obtained, we also determine the resolving power.
Table of Contents
- 1 Introduction
- 2 Basics
- 2.1 Preparation questions
- 2.2 Theoretical Basics
- 2.2.1 Derivation of the resolution power - Grid
- 2.2.2 Derivation of the resolution power - Prism
- 2.2.3 Diffraction vs. prism spectrum
- 3 Experimental setup and Realization
- 3.1 Experimental setup
- 3.2 Realization
- 4 Measurement results and evaluation
- 4.1 Measurement of the zero point
- 4.2 Measurement of the slit size - Prism
- 4.3 Measurement of the slit size - Grid
- 5 Conclusion
- 6 Data
- 6.1 Measuring the zero point
- 6.2 Measurement 2 - Prism
- 6.3 Measurement 3 - Grid
- 7 Sources
Objective & Thematic Focus
This experimental work aims to precisely measure the slit width of a telescope and concurrently determine its resolving power. The experiment utilizes spectral lines from an Hg-lamp, with a grating and a prism alternately placed between the lamp and the telescope's slit to analyze angular differences.
- Measurement of telescope slit width using spectroscopic methods.
- Determination of the resolving power of optical instruments.
- Comparative study of diffraction gratings and prisms in spectroscopy.
- Analysis of spectral lines from an Hg-lamp.
- Investigation of theoretical derivations for resolution power.
- Implementation and evaluation of an experimental setup in optics.
Excerpt from the Book
3.2 Realization
In the first step we try to measure the zero point of our slit. To get this value we need to find the exact spot where no more light passes through. We repeat the measuring process ten times to get an average value as well as an deviation.
At next we want to determine the slit size of our telescope. We can get this value by measuring the angle difference between the Hg and He lines of our lamp separated by a prism. This part of the experiment is repeated five times.
In the last part of our experiment, we measure the angular difference between the higher-order Hg lines. to do this, we place a grid between the lamp and the telescope so that we can distinguish the lines.
Summary of Chapters
1 Introduction: This chapter introduces the experimental goals, focusing on measuring the slit width of a telescope and determining its resolving power using an Hg-lamp, grating, and prism.
2 Basics: This section covers preparatory questions about resolution limits and provides theoretical derivations for the resolution power of both diffraction gratings and prisms, including a comparison of their spectra.
3 Experimental setup and Realization: This chapter details the required experimental components and outlines the step-by-step procedure for measuring the zero point of the slit, followed by determining the slit size using both a prism and a diffraction grating.
4 Measurement results and evaluation: This chapter presents and analyzes the collected experimental data, calculating the zero point, slit width for both prism and grid setups, and the resulting resolution power.
5 Conclusion: This chapter summarizes the findings, stating that the experimental values closely match theoretical predictions, with only minor deviations observed for both prism and grating measurements.
6 Data: This chapter provides the raw measurement data in tabular format, including values for zero point determination and measurements taken with both the prism and the diffraction grating.
7 Sources: This chapter lists the reference materials used in the experiment, specifically referencing a task sheet.
Keywords
Slit width, resolution power, Hg-lamp, grating, prism, spectral lines, angular difference, experimental setup, theoretical basics, data evaluation, zero point, diffraction, refraction, spectroscopy, optics.
Frequently Asked Questions
What is this work fundamentally about?
This work describes an experimental protocol focused on measuring the slit width of a telescope and determining its resolving power through the analysis of spectral lines using a grating and a prism.
What are the central thematic areas?
The central thematic areas include experimental optics, spectroscopy, diffraction, refraction, and the theoretical and practical aspects of optical resolution.
What is the primary objective or research question?
The primary objective is to measure the slit width of a telescope using an Hg-lamp's spectral lines and to derive the instrument's resolving power by analyzing angular differences obtained with a grating and a prism.
Which scientific method is used?
An empirical scientific method is employed, involving practical experimentation, systematic data collection, and quantitative evaluation based on established theoretical principles of physics.
What is covered in the main part?
The main part covers the theoretical foundations of resolution power for gratings and prisms, details the experimental setup and realization, and presents the measurement results along with their evaluation.
Which keywords characterize the work?
Key terms characterizing this work are slit width, resolution power, Hg-lamp, grating, prism, spectral lines, and experimental physics.
How is the resolution power derived for both a grid and a prism in the theoretical basics?
The theoretical basics section provides derivations for the resolution power of a grid based on intensity distribution and for a prism based on Fermat's principle and the refractive index, showing how these lead to specific equations.
What are the fundamental differences between a diffraction spectrum and a prism spectrum?
A diffraction spectrum features evenly spaced lines at small angles and is approximately linear in wavelength, often showing multiple orders, whereas a prism spectrum is non-uniform, non-linear, and typically displays only one spectrum.
What is the procedure for measuring the zero point of the slit?
To measure the zero point, the exact spot where no light passes through the slit is identified and measured ten times to obtain an average value and determine the deviation.
How is the slit size adjusted based on the zero point?
After calculating the slit size (B) from angular measurements, this value is adjusted by taking into account the previously determined zero point (z₀) to obtain the final adjusted slit width (B_adj).
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- Tim Peinkofer (Autor:in), 2025, Protocol AG. Resolution. Resolving Power and Slit Width via Hg Lamp Spectra, München, GRIN Verlag, https://www.grin.com/document/1688256
