Step 1: Understanding the Concept:
The question asks to identify a hand-held surveying instrument that is used specifically for setting out right angles (90°) with a higher degree of accuracy than simpler methods.
Step 2: Detailed Explanation:
Let's analyze the instruments listed:
(A) Cross staff: This is a simple instrument for setting out right angles. It consists of a frame or box with two pairs of vertical slits providing two lines of sight at 90° to each other. It is simple to use but has limited accuracy.
(B) Optical square: This is a more advanced and accurate hand instrument for setting out right angles. It works on the optical principle of reflection. It contains two mirrors (the horizon glass and the index glass) placed at an angle of 45° to each other. By the law of reflection, a ray of light that is reflected successively by two mirrors is deviated by an angle equal to twice the angle between the mirrors. So, $2 \times 45° = 90°$. To use it, the surveyor looks through the instrument at one ranging rod while another rod is moved until its image, reflected by the mirrors, is seen in line with the first rod. When this happens, the angle between the lines of sight to the two rods is exactly 90°. It is more accurate than a cross staff.
(C) Stadia: This is a method of distance measurement using a telescope with stadia hairs (two extra horizontal crosshairs). It is a method, not an instrument for setting out angles.
(D) Compass: A compass is used to measure magnetic bearings or directions relative to magnetic north. While you can set out a 90° angle by measuring bearings, it is not its primary or most accurate function for this specific task compared to an optical square.
Step 3: Final Answer:
The optical square is a compact hand instrument specifically designed for setting out right angles with greater accuracy than a cross staff. Therefore, option (B) is the correct answer.