Spherical Lenses

Concept:
Physics - Combination of Lenses.
Step 1: Identify focal lengths with sign convention.

• Convex lens ( ): +20 cm
• Concave lens ( ): -40 cm

Step 2: Calculate individual powers.
Power or .

• D
• D

Step 3: Find the total power of the combination.
The total power of lenses in contact is the algebraic sum of their individual powers: $ $

Step 1: Understanding the Concept:
This problem requires applying the thin lens formula to find the image positions for two different object distances. The shift in the image is the absolute difference between these two image positions.
Step 2: Key Formula or Approach:
The thin lens formula is:

Where:
= image distance
= object distance
= focal length
Sign convention: For a convex lens, is positive. Object distance is generally taken as negative.
Step 3: Detailed Explanation:
Initial case:
Focal length, cm.
Initial object distance, cm.
Let the initial image distance be .






(The negative sign indicates a virtual image formed on the same side as the object).
Final case:
The object moves 5 cm towards the lens.
New object distance, cm.
Let the new image distance be .





Shift in image:
The shift is the magnitude of the difference between the two image positions.




Step 4: Final Answer:
The image shifts by cm towards the lens.

Step 1: Understanding the Concept:
When multiple thin lenses are placed in close physical contact, the total effective power of the system is the algebraic sum of their individual powers.
A convex lens acts as a converging lens and has a positive focal length, meaning its optical power is also strictly positive.
Step 2: Key Formula or Approach:
The optical power of a single lens in diopters (D) is given by where is measured in centimeters.
For identical lenses placed in contact, the total effective power is .
Step 3: Detailed Explanation:
The focal length of a single convex lens is given as .
Calculating the power of one individual lens:
Because there are 5 identical lenses placed together in combination, we multiply the single power by 5:
Step 4: Final Answer:
The effective combined power of the lenses is .

Step 1: Use the formula for the magnetic moment.
The magnetic moment of a current-carrying loop is given by: where:
- is the current,
- is the area of the loop.

Step 2: Calculate the area of the loop.
The wire forms a circular loop, so the circumference of the loop is equal to the length of the wire. The circumference is: where is the radius of the loop. Since the total length of the wire is 6m: Now, calculate the area of the circle:
Step 3: Calculate the magnetic moment.
Now, substitute the current and the area into the formula for magnetic moment: Thus, the magnetic moment of the loop is: