Reference guide
Physics · Optics · Engineering — six techniques and ready-to-copy templates for getting precise, auditable solutions from an AI language model. Built for students, tutors, engineers, and technically curious users who want cleaner setup, better unit tracking, and fewer hidden math mistakes.
Best general-purpose STEM prompt
Use this when you want one reliable default prompt for physics, optics, engineering, or applied math problems.
You are solving a physics or engineering problem. 1. List knowns and unknowns with units. 2. Identify the governing law or equation. 3. State assumptions and sign conventions. 4. Solve algebraically before substituting numbers. 5. Substitute values with units. 6. Check dimensional consistency and reasonableness. 7. Give the final answer clearly. Problem: [paste problem here]
Show-your-work prompting
Ask the model to show the key intermediate calculations, units, assumptions, and checks before giving the final answer. The goal is not hidden reasoning; the goal is an auditable solution path that makes formula choice, substitutions, and unit handling easier to verify.
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Zero-shot trigger phrase
Append this to any question: "Solve this step by step. Show the governing equations, substitutions, units, intermediate numerical results, and final answer. Keep the reasoning concise but complete enough to audit."
Full CoT template for physics
You are solving a physics problem. Show the work clearly: 1. List all known variables with units. 2. Identify the governing equation(s). 3. State assumptions and sign conventions. 4. Solve algebraically before substituting numbers. 5. Substitute values and compute each step. 6. Check units using dimensional analysis. 7. State the final answer with correct significant figures and units. Problem: [paste your problem here]
Step-back prompting
Before solving, ask the model to first identify the underlying physics principles or engineering concepts involved. Grounding in first principles reduces hallucinations and ensures the right formula family is invoked. In the original Step-Back Prompting paper, the method improved PaLM-2L results on MMLU Physics and Chemistry by 7 and 11 percentage points, respectively.
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Two-phase template
— Phase 1: Principle extraction — "You are an expert physicist. What are the fundamental principles and governing equations relevant to solving the following problem? Do not solve it yet. Problem: [your problem]" — Phase 2: Guided solution — "Given those principles: [paste Phase 1 output] Now solve the problem step by step, explicitly applying each principle you identified."
Role prompting
Assign the model an expert persona relevant to your problem. This steers the model toward domain-specific vocabulary, correct formula selection, and appropriate precision. The more specific the role, the more calibrated the output — "senior optical engineer" elicits different behavior than just "physicist."
Effective role descriptions for STEM
Role + CoT combined template
You are a [ROLE]. A student presents you with the following problem. Solve it step by step at an upper-division undergraduate level: — Identify relevant physical laws. — Set up the governing equations. — Solve algebraically, then numerically. — Verify the answer with a sanity check or dimensional analysis. — Note any assumptions made. Problem: [your problem]
Few-shot prompting
Provide one or two fully worked examples before your actual question. The model learns the desired format, level of rigor, and notation style from those examples — extremely useful when you need consistent output structure across a set of similar problems.
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One-shot optics template
Solve optics problems using this exact format:
EXAMPLE:
Problem: An object is 30 cm in front of a concave
mirror with focal length 10 cm. Find image distance.
Known: u = -30 cm, f = -10 cm (mirror convention)
Equation: 1/v + 1/u = 1/f
Solve: 1/v = 1/f - 1/u
= 1/(-10) - 1/(-30)
= -3/30 + 1/30 = -2/30
Result: v = -15 cm (real image, 15 cm in front)
Check: |m| = |v/u| = 15/30 = 0.5 ✓
Now solve using the same format:
Problem: [your problem]
Program of thought (PoT) prompting
Ask the model to express the solution as executable Python code rather than prose arithmetic. This offloads numerical computation to an interpreter, eliminating floating-point reasoning errors that LLMs can make. Ideal for problems with many numerical substitutions or iterative calculations.
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PoT template
Solve the following engineering/physics problem by writing Python code. Requirements: — Define all known variables with comments showing units. — Use scipy or numpy if needed. — Print each intermediate result labeled with its physical meaning and units. — Print the final answer clearly. — Do not use symbolic libraries; compute numerically. Problem: [your problem]
Meta prompting
Instead of solving a specific problem, define a reusable procedural template the model should follow for any problem of a given type. Think of it as writing a solver specification rather than a one-off question. Pair it with self-consistency (run the same prompt 2–3 times and compare answers) for high-stakes calculations.
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Meta template — 7-step STEM solver
When I give you a physics or engineering problem, always follow this procedure: Step 1 — Classify: identify the domain (mechanics, optics, thermodynamics, etc.) Step 2 — Draw: describe a labeled diagram or free-body diagram in words. Step 3 — Formulate: list all applicable equations with variable definitions. Step 4 — Solve: work algebraically before substituting numbers. Step 5 — Compute: substitute values, track units at every step. Step 6 — Verify: dimensional analysis + order-of-magnitude sanity check. Step 7 — Summarize: one-line result with value, units, and direction (if a vector). Acknowledge this procedure, then wait for my first problem.
Verify important answers independently. For graded work, engineering decisions, or safety-critical calculations, check the final result with a trusted source, calculator, code, or human expert. AI models can still choose the wrong equation, mishandle signs, or make arithmetic mistakes.
Always state units and sign conventions explicitly. Never assume the model will choose your convention. Write "u = −30 cm (object distance, negative = real object)" rather than just "u = 30 cm."
Separate known variables from unknowns. List them before the question: "Given: λ = 550 nm, d = 0.3 mm, L = 1.2 m. Find: fringe spacing Δy."
Request dimensional analysis as a mandatory check. Add: "After computing the final answer, verify it is dimensionally consistent." This catches formula-selection errors before they reach you.
Use self-consistency for critical results. Run the same prompt 2–3 times. If answers diverge, ask the model to identify which step differs and resolve the conflict explicitly.
Building this structure into any prompt aligns the model with how expert physicists actually approach problems — reducing both formula-recall errors and reasoning shortcuts.
Phase 1
Problem representation
Phase 2
Strategy selection
Phase 3
Strategy execution
Phase 4
Evaluation
Solve this problem in 4 phases: 1. Representation — restate the problem in your own words, draw a word diagram, list knowns/unknowns. 2. Strategy — identify which law or principle applies and why; rule out alternatives. 3. Execution — solve step by step with units at every line. 4. Evaluation — does the answer make physical sense? Check limiting cases if applicable. Problem: [your problem]