The student sets up the apparatus with a screen placed at a distance $D=90.0cm$ from an illuminated, upright triangular object. Two positions of the lens produce a sharp image on the screen:

• Position 1 (lens closer to the object): the actual object distance is $X=22.0cm$. This produces a magnified, inverted image.
• Position 2 (lens moved further from the object): the actual object distance is $Y=68.0cm$. This produces a diminished, inverted image.

(i) Describe how the second image (at Position 2) differs in appearance (orientation and relative size) from the original upright triangular object.

(ii) Calculate the distance $d=Y-X$.

(iii) Calculate the focal length $f_1$ of the lens using the equation:

Give your answer to 3 significant figures.

The student repeats the procedure for an object-to-screen distance $D=100.0cm$. The student records:

(i) Calculate the new distance $d$ for this setup.

(ii) 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 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.

(i) State one technique to use when doing this type of experiment to ensure that the image on the screen is focused as clearly as possible.

(ii) Explain why this experiment is usually done in a darkened room.