Final answer:
The correct answer for measuring roughness height is a d) profilometer, which is specifically designed to evaluate surface roughness profiles, including roughness height, in high detail.
Step-by-step explanation:
The student's question pertains to the measurement of roughness height, which is a parameter used to quantify the roughness of a surface in engineering applications. The profilometer is the correct instrument for measuring surface roughness; it is designed to characterize the surface profiles and provide accurate measurements of surface roughness parameters, including roughness height.
A profilometer can be a contact or non-contact device that traverses a surface and records the vertical deviations to determine the roughness. Other tools, such as a dial indicator, micrometer, or optical comparator, are not specifically used for this purpose. A dial indicator can measure small distances or movements, a micrometer measures thickness or diameters with a very high accuracy, and an optical comparator magnifies an object to compare its size or shape against a standard. Therefore, the letter that correctly completes the sentence is (d) profilometer.