Snell

{
  "asOf": "2026-10-11T08:56:14.063Z",
  "brewsterAngleDeg": 53.11517,
  "criticalAngleDeg": null,
  "degraded": false,
  "deviationDeg": 12.952771,
  "disclaimer": "Screening signal computed from the named public source. Not financial, legal or investment advice; provided as is. Verify at the source before acting.",
  "incidentAngleDeg": 45,
  "medium1": "air",
  "medium2": "water",
  "n1": 1.000293,
  "n2": 1.333,
  "notChecked": [
    "wavelength dependence (dispersion): the index of real glass and water varies with colour by about 1%",
    "reflected light intensity (Fresnel equations) and polarisation",
    "…1 more"
  ],
  "reasons": [
    "Snell's law: n1 sin(theta1) = n2 sin(theta2).",
    "Entering a denser medium bends the ray toward the normal."
  ],
  "refractedAngleDeg": 32.04722871,
  "source": "computed locally",
  "speedRatioV2OverV1": 0.75040735,
  "summary": "Light going from n = 1.000293 to n = 1.333 at 45 degrees bends to 32.0472 degrees.",
  "verdict": "REFRACTS"
}

# bash or zsh: see the payment challenge. Nothing is charged.
curl -sS -g -i 'https://physics-calc.x402tookit.com/snell?incidentAngleDeg=45&n1=air&n2=water'

# x402 v2 sends the challenge base64-encoded in the PAYMENT-REQUIRED header (v1 sends it in the body).
# To read the header:
curl -sS -g -o /dev/null -D - 'https://physics-calc.x402tookit.com/snell?incidentAngleDeg=45&n1=air&n2=water' \
  | grep -i '^payment-required:' | cut -d' ' -f2 | tr -d '\r' | base64 --decode

// npm i @x402/fetch @x402/evm viem
import { wrapFetchWithPayment, x402Client } from "@x402/fetch";
import { registerExactEvmScheme } from "@x402/evm/exact/client";
import { privateKeyToAccount } from "viem/accounts";

// Pays at most $0.02 per call.
const client = new x402Client().setSpendControls({ maxAmountPerPayment: "$0.02" });
registerExactEvmScheme(client, { signer: privateKeyToAccount(process.env.EVM_PRIVATE_KEY) });
const pay = wrapFetchWithPayment(fetch, client);

// Not sure it's safe to pay? ToolVet checks it first for $0.005. Pay for that from a separate
// client: this one is capped at $0.02 per payment. GET https://toolvet.app/api/v1/check?url=https%3A%2F%2Fphysics-calc.x402tookit.com%2Fsnell
const res = await pay("https://physics-calc.x402tookit.com/snell?incidentAngleDeg=45&n1=air&n2=water");
console.log(res.status, await res.text());

# pip install "x402[requests,evm]"
import os
from eth_account import Account
from x402 import x402ClientSync
from x402.http.clients import x402_requests
from x402.mechanisms.evm import EthAccountSigner
from x402.mechanisms.evm.exact.register import register_exact_evm_client

# Pays at most $0.02 per call.
client = x402ClientSync().set_spend_controls({"max_amount_per_payment": "$0.02"})
register_exact_evm_client(client, EthAccountSigner(Account.from_key(os.environ["EVM_PRIVATE_KEY"])))

with x402_requests(client) as session:
    res = session.get("https://physics-calc.x402tookit.com/snell?incidentAngleDeg=45&n1=air&n2=water")
    print(res.status_code, res.text)