The student sets up the apparatus such that:

• The distance $D$ between the illuminated object (an upward-pointing arrow $\uparrow$) and the screen is 90.0 cm.
• The lens is initially placed close to the illuminated object.
• The lens is moved away from the illuminated object until a magnified, inverted, sharp image of the object is formed on the screen. The actual object distance from the lens is $X=23.5cm$.

The student then continues to move the lens further away from the illuminated object until a second sharp image, which is diminished and inverted, is formed on the screen. The actual object distance is now $Y=66.5cm$.

(i) Describe the appearance of the second sharp image formed on the screen in terms of its orientation and relative size compared to the original object. (ii) Calculate the value of $d=Y-X$. (iii) The focal length $f_1$ of the lens can be found using the equation:

Calculate the value of $f_1$. Give your answer to 3 significant figures.

The student repeats the procedure for an object-to-screen distance $D=110.0cm$ and records the following results:

• $X=20.8cm$
• $Y=89.2cm$
• $d=68.4cm$

Calculate a second value, $f_2$, for the focal length of the lens using the same equation. Give your answer to 3 significant figures.

Two quantities can be considered to be equal within the limits of experimental accuracy if their values are within 10% of each other. State whether your values of $f_1$ and $f_2$ can be considered equal. Support your statement with a calculation.

This experiment is usually performed in a darkened room. Explain how this makes it easier to determine when the image is in sharp focus.