Draw a ray diagram to show how a converging lens can cause spherical aberration - AQA - A-Level Physics - Question 1 - 2022 - Paper 4

For drawing a labelled ray diagram for an astronomical refracting telescope:

1. Sketch the Telescope: Draw two convex lenses in the same vertical alignment, separated by a distance to represent the tube of the telescope.

2. Label Lenses: Label the lens closer to the object as the objective lens and the one closer to the observer as the eyepiece lens.

3. Draw Principal Foci: On both sides of each lens, mark the principal foci and label them as F1 for the objective and F2 for the eyepiece.

4. Draw Non-Axial Rays:

   • Draw three non-axial rays from a distant object (like a star) passing through the objective lens:
     • The first ray travels parallel to the principal axis, refracting through F1.
     • The second ray originates from the same object but is drawn at a slight angle, bending as it reaches F1.
     • The third ray passes through the top edge of the lens, also converging at F1.

5. Passing Through Eyepiece: Mark the intersection points of rays at the focus of the objective lens as they approach the eyepiece lens. Draw them spreading out through the eyepiece lens. Finally, indicate the eye's position at the end of the tube to demonstrate observation.

6. Labeling: Clearly label the principal foci (F1 and F2) and include the construction lines for clarity.

To calculate the focal length of the eyepiece lens:

1. Given Values:

   • For a telescope, L = 1.74 m (distance between lenses) and M = 750 (angular magnification).

2. Formula: The angular magnification is given by: $M = \frac{f_o}{f_e}$ where f_o is the focal length of the objective lens and f_e is the focal length of the eyepiece lens. We can also express the total length as: $L = f_o + f_e$

3. Express f_o in terms of f_e: Rearranging gives: $f_o = M \cdot f_e$

4. Setting up the equation: Substitute this back into the total length equation: $L = M \cdot f_e + f_e$ This simplifies to: $L = (M + 1) \cdot f_e$

5. Solving for f_e: Replacing L with 1.74 m and M with 750, we have: $1.74 = (750 + 1) \cdot f_e$ $f_e = \frac{1.74}{751} \approx 0.00232 m$

6. Final Result: Thus, the focal length of the eyepiece lens is approximately: $f_e \approx 0.00232 m$

The James Lick telescope can identify binary stars through the following techniques:

1. Using Processed Images: The telescope captures images that are processed using a Charged-Coupled Device (CCD). This image processing allows for better resolution and clarity of the stars in question.

2. Direct Observation: Astronomers can also observe the binary stars directly using the naked eye through the eyepiece. This method may provide immediate observations of double star systems.

3. Combining Techniques: Utilizing both methods allows for a thorough analysis of the binary stars, as processed images can reveal details that might not be seen in direct observations alone. The combination enhances the overall observational efficacy of the telescope.