The speed of light is not directly from the Samhita. It is given by Sayana in commenting 1.50.4 verse of RigVeda. The devata of the verse is Surya. The verse is:
तरणिविश्वदर्शवो ज्योतिष्कृदसि सूर्य । विश्वमा भासि रोचनम् ।।
Swift and all beautiful art thou, O Surya, maker of the light, Illuming all the radiant realm.
As it talks about maker of light. Commentary of Sayana in this verse is as:
तथा च स्मर्यत योजनानां सहस्रम् द्वे द्वे शते द्वे च योजने । एकेन निमिषार्धेन क्रममाण नमोऽस्तु ते ॥
tathA cha smaryata yojanAnAM sahasram dve dve shate dve cha yojane | ekena nimiShArdhena kramamANa namo.astu te ||
It is remembered, [O Sun] bow to you, you who traverse 2,202 yojanas in half a nimesha.
Here it is talking about speed of Sun. But as it is in the commentary of verse containing maker of light, it is taken as speed of light.
Here by calculation from Purana we know 1 nimisha = 16/75 seconds.
For eg. 2.8 of Vishnu Purana says:
Fifteen twinklings of the eye (Nimeshas) make a Káshthá; thirty Káshthás, a Kalá; thirty Kalás, a Muhúrtta (forty-eight minutes); and thirty Muhúrttas, a day and night: the portions of the day are longer or shorter, as has been explained; but the Sandhyá is always the same in increase or decrease, being only one Muhúrtta. From the period that a line may be drawn across the sun (or that half his orb is visible) to the expiration of three Muhúrttas (two hours and twenty-four minutes), that interval is called Prátar (morning), forming a fifth portion of the day.
The summary is:
15 nimesha = 1 kastha
30 kastha =1 kala
30 kala = 1 muhurta
30 muhurta = 1 day-and-night
Thus 1 nimisha = 86400/(30×30×30×15) =16/75 sec.
Thus half-nimisha= 16/150 seconds.
But the distance yojana is highly debatable when converted to metre. Using 1 yojana= 9 mile (which is a general standard value). The value of Yojana is difficult in conversion. It is because value are defined as this way. For eg. In Markandaye Purana.
10 Paramáńus = 1 Parasúkshma; 10 Parasúkshmas = 1 Trasareńu;
10 Trasareńus = 1 particle of dust, or Mahírajas; 10 Mahírajasas = 1 Bálágra, 'hair's
point;' 10 Bálágras = 1 Likhyá; 10 Likhyás= 1 Yúka; to Yúkas = 1 heart of barley
(Yavodara); 10 Yavodaras = 1 grain of barley of middle size; 10 barley grains = 1 finger,
or inch; 6 fingers = a Pada, or foot (the breadth of it); 2 Padas = 1 Vitasti, or span; 2
spans = 1 Hasta, or cubit; 4 Hastas = a Dhanu, a Danda, or staff, or 2 Nárikás; 2000
Dhanus = a Gavyúti; 4 Gavyútis = a Yojana.
Thus it is very difficult to convert exact value of Yojana. Standard value is taken as 8-9 miles. It is obtained as:
Normally 1 hasta= 45 cm. (Hasta is length of hand from elbow to tip of middle finger)
We can measure it. Also see Hasta here
Thus from above Puranic data.
1 yojana = 45×4×2000×4 = 1440000 cm = 9 miles
Speed=2202×9×150/16= 185793 miles/ second.
The standard scientific value for speed of light is 186322 miles/ second.
Thus they are pretty close together.
The points to be considered here are:
-- The verse itself do not mention the value as speed of light. But as it is in the commentary of "maker of light" people have associated it with speed of light.
-- The value of yojana is a debatable value.